Preheat oven to 350 degrees F (175 degrees C). Grease an 8-inch square pan.
Combine oats, brown sugar, white sugar, baking powder, salt, and cinnamon together in a bowl. Whisk milk, eggs, canola oil, and vanilla extract together in a separate bowl. Stir egg mixture into oats mixture until well combined; set aside until flavors blend, about 20 minutes. Spread oats mixture into prepared square pan.
Bake in the preheated oven until edges are golden brown, about 30 minutes.