Preheat an oven to 350 degrees F (175 degrees C). Spray a 9×13-inch baking pan with cooking spray.
Arrange the peaches in the prepared pan. Scatter the butter over the peaches, then sprinkle the brown sugar evenly on top. Set aside. Mix flour, white sugar, baking powder, and salt in a bowl. Stir the oil into the beaten eggs, then stir the egg mixture into the dry ingredients. Spoon the batter over the peaches, then sprinkle cinnamon on top.
Bake in the preheated oven until the crust is lightly browned, about 45 minutes.