Whisk flour, brown sugar, white sugar, baking powder, cinnamon, and salt together in a bowl until no lumps remain.

Stir milk, vegetable oil, and vanilla extract into flour mixture until batter just combined.

Beat egg whites in a large glass or metal mixing bowl until soft peaks form. Lift your beater or whisk straight up: the egg whites will form soft mounds rather than a sharp peak. Fold into batter.

Preheat a waffle iron according to manufacturer's instructions. Coat with cooking spray.

Cook, in batches, in the preheated waffle iron until crisp and golden brown, about 2 minutes. Repeat with remaining batter.