Place an oven rack in the middle position. Preheat the oven to 350°F (180°C). Spray a 9-inch square nonstick pan with baking spray.
In a medium bow, whisk together the flour, brown sugar, cocoa, granulated sugar, baking soda, and salt. 2 cups (285 g) all-purpose flour ¾ cup (150 g) packed light brown sugar ⅔ cup (55 g) unsweetened cocoa powder ½ cup (100 g) granulated sugar 1 ¼ teaspoons baking soda ½ teaspoon salt
In a second large bowl, whisk together the oil, vinegar, vanilla and water. ½ cup (120 mL) vegetable oil 4 teaspoons vinegar 2 teaspoons vanilla extract 1 ⅓ cup (320 mL) water
Add the flour mixture to the oil mixture. Stir just until combined. Do not overmix. Pour batter into the prepared pan, smoothing the top.
Bake until just firm and a toothpick inserted into the center comes out with moist crumbs, 25 to 30 minutes. Place the cake to cool completely on a wire cooling rack.
Once the cake has completely cooled, top with frosting is using.