Preheat oven to 350°. Line a 17"-by-11" rimmed baking sheet with parchment paper.
In a medium microwave-safe bowl, microwave granulated sugar, semisweet chocolate, and water in 20-second increments, stirring in between, until chocolate is melted and mixture is smooth. Stir in oil, cocoa powder, vanilla, and salt until smooth. Let cool slightly, then stir in egg whites. Fold in flour and baking powder just until combined.
Evenly spread batter onto prepared baking sheet. Sprinkle with chips and half of candy cane pieces.
Bake, rotating pan every 10 minutes, until firm in the center, 25 to 30 minutes. Using parchment, lift brownie off baking sheet and transfer to a cutting board. While still hot, slice into squares with a sharp knife. (Brownie brittle will become crisper as it cools.)
In a small microwave-safe bowl, microwave white chocolate in 10-second increments, stirring in between, until melted and smooth. Drizzle over cooled brownie brittle and sprinkle with remaining candy cane pieces.
Make Ahead: Undecorated brownie brittle can be made 1 month ahead. Let cool, transfer to an airtight container, and freeze.