Clean your raspberries by rinsing them with cool water. Check inside each one for any debris to remove. Set your 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 as handles later. Grease the foil, making sure to get the sides.
Cut up your butter into pieces and add them to a 2-quart glass batter bowl or microwave-safe mixing bowl. Heat the butter on high for a minute, covered.
Add your 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 your brown sugar and salt to the bowl and beat with a mixer until blended.
Add your vanilla. Then add one egg at a time, beating well after each addition.
Stir in your flour and cocoa, just until combined.
Gently stir in your white chocolate chips.
Gently pat your 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, 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 your brownies and transfer them to a large cutting board. Cut the brownies into the size you desire.
Store the brownies in the refrigerator for the best consistency. (They'll get too gooey at room temperature.) They can stay for several days in the refrigerator. You can freeze the brownies in plastic freezer bags and wait a couple minutes before eating them frozen. (They'll taste like fudge bars!)
These are even better the next day, so if you can, make them ahead of time and keep them in the refrigerator.