Make the starter. Add the starter ingredients to a medium mixing bowl. Stir with a spoon to combine well. Cover the bowl with plastic wrap and refrigerate it overnight (8-12 hours).
Cut up the apricot slices into little pieces. Soak them with the raisins overnight at room temperature by adding them to a small bowl with the rum and covering them. See notes.
The Next Day
An hour before you begin making the recipe, take out the starter to sit at room temperature. Take out the butter to soften. Take out four large eggs; leave two whole at room temperature and separate two eggs so the yolks can sit at room temperature. (Refrigerate the whites for another use.)
Drain the raisins and apricot pieces by placing them in a fine-mesh strainer over a small pan if you want to save the rum to drink. Zest the orange and lemon and set the zest aside. (Refrigerate the zested fruit for another use.)
Add the starter (it will be sticky like taffy) to the bowl of a stand mixer. Add the room-temperature 2 eggs and 2 egg yolks. Mix with a dough hook attachment until combined, for about two minutes. (You can start at speed 2, then increase to 3, then 4.) Add 2 ⅛ cups of bread flour and mix with the dough hook for 90 seconds (use speed 2 or 3) until the dough is combined in a ball, mostly pulled away from the sides of the bowl and sticky.
Add 1 ½ teaspoons of salt and ¾ cup of sugar. Mix with the dough hook on speed 2 or 3 until the dough is shiny and smooth, for 4-5 minutes. Scrape down the sides of the bowl and the hook as needed. The dough will be softer, stretchier and ribbon-like at this point. It will be sticking to the bowl.
Add the vanilla and orange extracts and mix in on speed 2 briefly.
Check if the butter is soft. If not, put it in the microwave on defrost for just a few seconds. Add one piece of softened butter at a time to the stand mixer, mixing after each addition on the lowest setting, then increasing to speed 2. You may still see pats of butter that haven't blended, but that's okay for now. Stop to scrape down the sides of the bowl with a spatula as needed.
If more than a three-inch circle of dough is sticking to the bowl in the center, add ⅛ cup more flour and mix. Scrape down the sides of the bowl so the dough comes together. If that's still not enough, add another tablespoon or so of flour, being careful not to add too much flour, or it will be dense. Knead the dough on speed 3 for eight minutes.
Let the dough rest for a minute and pat the raisins and apricots dry with paper towels. Add the dried fruit and all of the zest to the bowl of dough. Knead with a dough hook on speed 2 for 5-6 minutes, until all of the fruit is mixed in well. It should not just be sticking to the surface of the dough but incorporated inside it. Scrape down the dough hook as needed.
Prepare a clean surface on your counter (not wood) or use a sheet pan. Spray the surface with cooking spray. Spray the surface of the dough with cooking spray and spray your hands as well. Transfer the dough to the sheet pan or counter. Stretch the dough a bit to the sides, then fold it in half (this incorporates air.) Stretch the dough again and fold it in half. Use a dough cutter or straight-edged knife to divide the dough in half.
Grease two 5-inch paper panettone molds with cooking spray. Gather each section of dough into a mound (it'll be very sticky) and place each into a panettone mold (the dough should fill the mold half-way.) Let the dough rise in the molds at room temperature for another hour, covered with large bowls so there is room at the top.
When there is about 20 minutes left for the dough to rise, prepare the oven by removing the top rack, leaving space above the middle rack. Preheat the oven to 350 degrees F.
When the dough is done rising, make the egg wash. Beat one egg. Brush some of it on the surface of the dough in each panettone mold. (Discard any extra egg wash.) Use a straight-edged knife to score the top of each panettone by making an X-shaped cut on the surface.
Place the panettone molds on a sheet pan and bake on the center rack for 50-60 minutes, or until the surface is a deep brown and a cake tester placed straight down in the center comes out clean. If you have one panettone mold with more dough in it than the other, it will take longer to bake.
Leave the panettone in the molds. Insert two wooden skewers into the lower section of each mold, 2-3 inches apart, so that the skewers are sticking out on each side by a couple of inches. Let the panettone hang upside down for about 2 hours, until fully cooled. Do this by hanging each panettone upside down between two tall glass canisters or two tall cans of bread crumbs and letting the skewers rest on the tops of the containers. This prevents the panettone from sinking and allows it to become even taller.
The panettone is freshest on the first day. You can freeze the cooled panettone by wrapping it in plastic then placing it in a freezer bag (slice it first if you wish) to keep it fresh.
If you prefer to store leftover panettone at room temperature, wrap it tightly in plastic. (It helps to add a wedge of apple in there to keep it moist.) Then place the wrapped panettone in a sealed plastic bag. It should be eaten the next day or two before it gets too dry. Warming it a bit in the microwave helps to make it softer. You also can make French toast with the leftover panettone.
Notes
See the step-by-step photos in the article that goes with this recipe.This new and improved recipe produces panettone that's closer to a brioche bread but is still a cross between bread and pound cake. It would take days of preparation to make the kind of panettone that's sold in stores. Soaking the raisins and dried apricots in rum plumps them and imparts flavor and moisture to the panettone. For a non-alcoholic version, soak them in water. If you don't soak the raisins, they'll pull moisture away from the panettone and make it dry.