Preheat the oven to 350˚. Line a 13-by-18-inch rimmed baking sheet with foil, leaving a small overhang on all sides. Lightly coat the foil with cooking spray. Whisk the flour, cocoa powder, baking powder and salt in a medium bowl.
Whisk the melted butter, vegetable oil, granulated sugar and brown sugar in a large bowl. Whisk in the eggs, one at a time, then the vanilla. Add the flour mixture and stir with a rubber spatula until just combined. Spread the batter evenly in the prepared pan, all the way to the edges.
Bake until a toothpick inserted into the center of the brownies comes out clean with a few crumbs, 15 to 18 minutes. Transfer to a rack and let cool about 30 minutes in the pan, then freeze until firm, about 45 minutes.
Invert the brownies onto a cutting board and remove the baking sheet. Peel off the foil and use it to reline the baking sheet. Trim about ¼ inch from all four sides of the brownies. Cut the brownies in half crosswise. Lay one half on the prepared pan. Working quickly, scoop all the ice cream on top of it and spread evenly with an offset spatula all the way to the edges. Place the other brownie half on top and press down gently; smooth the sides with the offset spatula. Wrap the foil around the brownie sandwich and freeze until hardened, at least 6 hours or overnight.
Cut the brownie sandwich in half lengthwise, then crosswise into sixths. Press the sides of each sandwich into the nonpareils. Freeze until ready to serve.