Clean the raspberries by rinsing them with cool water. Check inside each one for any debris to remove. Set the raspberries, hole-side down, in a single layer on paper towels to dry.
Preheat your oven to 350 degrees F. Grease a 9x13 baking pan with cooking or baking spray. Line the pan with foil, with extra overhanging on each end, so you can fold it around the edges of the pan and use it as handles later. Grease the foil, making sure to get the sides.
Cut up the butter into pieces and add them to a 2-quart glass bowl or microwave-safe mixing bowl. Heat the butter on high for a minute, covered.
Add the bittersweet and semisweet chocolate chips to the bowl (save the white ones for later.) Heat the chocolate and butter for 30 seconds on high, then stir. Heat for another 15 seconds or so, just until the chocolate melts. Stir to combine.
Add the brown sugar and salt to the bowl and beat with a mixer until blended.
Add the vanilla. Then add one egg at a time, beating well after each addition.
Stir in the flour and cocoa, just until combined.
Gently stir in the white chocolate chips.
Gently pat the raspberries with a paper towel to remove excess moisture. Add half of the raspberries to the batter and gently stir them in, trying not to break them.
Transfer the brownie batter to your baking ban. Smooth it with a spatula until it's even. Place the rest of the raspberries on top of the batter, open ends facing up, in a single layer.
Bake for 35-40 minutes, or until a toothpick inserted in the center comes out with moist crumbs.
Let the pan cool on a wire rack. Then refrigerate the pan of brownies for 2-3 hours to chill and set. When you're ready to cut them, use the foil handles to lift out the brownies and transfer them to a large cutting board. Cut the brownies into the size you desire. I recommend small portions, since they're rich.
Store the brownies in the refrigerator for the best consistency. (They'll get too gooey at room temperature.) They can stay for up to three days in the refrigerator. You also can freeze the brownies in an airtight container, separating each layer with wax paper or parchment paper. Eat them within three months, for best quality.
Notes
Raspberries: I always use fresh raspberries, but you could use frozen ones. I would pat them dry first. You shouldn't need to thaw them.Butter: This recipe calls for salted butter, but you can use unsalted if you add a little extra salt to the batter. You'd need an extra ¼ teaspoon of salt per stick of butter.These brownies are even better the next day, so if you can, make them ahead of time and keep them in the refrigerator.