Preheat the oven to 350 degrees F. Spritz 2 canoe pans with nonstick baking spray.
Whisk the flour, granulated and brown sugar, baking powder, and salt together in a large bowl until no lumps remain.
Whisk the oil, water, vanilla, and egg yolks together in a separate bowl. Stir into the dry ingredients and set aside.
With an electric hand mixer or stand mixer fitted with the whisk attachment, whip the egg whites into stiff peaks on medium-high speed, adding the cream of tartar once the egg whites are frothy.
Gently fold the egg whites into the batter, working slowly to incorporate them evenly.
Pour the batter into the prepared canoe pans, filling each well only halfway.
Bake for 18-20 minutes until the cakes are golden brown and a tester inserted into the center of a cake comes out clean.
Cool the cakes for 10 minutes on a wire rack.
Line the rack with waxed paper and lightly spritz the paper with more nonstick baking spray.
Carefully remove the cakes from the baking pans and cool completely on the waxed paper-lined rack.