Preheat oven to 350 degrees. Butter a 9-inch square baking pan. Line with parchment, leaving a 2-inch overhang on two sides; butter parchment.
In a medium bowl, whisk together flour, baking powder, and salt. In a heatproof bowl set over a pot of simmering water, melt chocolate and butter with oil. Remove from heat. Add both sugars and whisk 10 seconds.
Add eggs and whisk vigorously until glossy and smooth, 45 seconds. Using a rubber spatula, stir in dry ingredients. Pour batter evenly into prepared pan, smoothing top with spatula.
Bake until set and a tester inserted in center comes out with moist crumbs, 35 to 40 minutes. Let cool in pan on a wire rack for 20 minutes, then remove using parchment; let cool completely on rack before cutting into squares.
Brownies can be stored in an airtight container up to 2 days.