Heat oven to 350° F. Butter an 8-inch square baking pan. Line with 2 crisscrossed pieces of parchment, buttering in between and leaving an overhang on all sides; butter the parchment.
In a medium bowl, whisk together the flour, cocoa, baking powder, and salt; set aside.
In a large microwave-safe bowl, combine the butter and semisweet chocolate. Microwave on high in 30-second intervals, stirring between each, until melted and smooth. Let cool slightly. Whisk in the sugar, eggs, and vanilla until smooth.
Add the flour mixture and mix until just combined (do not overmix).
Spread the batter in the prepared pan and bake until a toothpick inserted in the center comes out clean, 30 to 35 minutes. Let cool completely in the pan.
In a medium microwave-safe bowl, microwave the white chocolate and oil in 30-second intervals, stirring between each, until melted and smooth. Spread on top of the cooled brownies. Sprinkle with the candies and let set.
Holding the paper overhang, lift the brownies out of the pan and transfer to a cutting board. Cut into 16 squares (4 rows by 4 rows).