Mix flour, white sugar, milk, peanut butter, 2 tablespoons cocoa powder, vegetable oil, vanilla extract, baking powder, and salt together in a bowl until batter is smooth; spread into an 8x8-inch microwave-safe dish.
Mix water, brown sugar, and 1/4 cup cocoa powder together in a bowl until dissolved; pour over batter.
Cook at 50% in microwave for 9 minutes. Rotate dish 1/2 turn and microwave on high until set, about 6 more minutes.