Preheat the oven to 350 degrees F. Grease and line an 8x8-inch square baking pan with parchment paper or greased aluminum foil, leaving an overhang to help lift the brownies out later.
Put 1 cup Mini Reese's Peanut Butter Cups, roughly chopped into a freezer-safe bag and place in the freezer while the brownie batter comes together.
In a medium saucepan over low heat, melt 1 cup unsalted butter and 4 ounces bittersweet chocolate, chopped together, stirring until smooth and glossy. Remove from the heat and let cool for 5 minutes.
In a large mixing bowl, add 1/4 cup white sugar, 1 1/2 cups light brown sugar, and 3 large eggs. Beat on medium-high speed until pale and voluminous, about 2 to 3 minutes. Add 2 teaspoons vanilla extract and the cooled melted chocolate. Beat on low speed until uniform in color.
Sift in 3/4 cup all-purpose flour, 1/2 cup unsweetened cocoa powder, sifted, and 3/4 teaspoon salt. Gently fold into the batter using a rubber spatula until just combined. Do not overmix.
Fold in the frozen, chopped Reese's. The freezing helps them hold their shape during baking.
Pour the batter into the prepared pan and smooth the top. Bake for 30 minutes, or until the edges are set and a toothpick inserted into the center comes out with a few moist crumbs. The center should still look slightly underdone.
As soon as the brownies come out of the oven, scatter 1/2 cup Mini Reese's Peanut Butter Cups, roughly chopped over the top. Cool completely in the pan before turning out.
For clean slices, chill the cooled brownies in the refrigerator for 30 minutes before cutting with a sharp knife. Wipe the knife between cuts. Slice into 2 inch by 2 inch squares.