Stir white sugar and 1 tablespoon brown sugar together in a small bowl. Stir flour, cinnamon, pumpkin pie spice, and salt together in a separate bowl with a whisk.
Put butter in an 8-inch cake pan and melt in preheated oven, 3 to 5 minutes.
Sprinkle remaining brown sugar over the melted butter in the cake pan.
Beat eggs, milk, vanilla extract, and almond extract together in a larger bowl with an electric mixer; stir into the flour mixture until you have a smooth batter. Pour the batter over the butter and brown sugar in the cake pan. Sprinkle white and brown sugar mixture over the batter.
Bake in the preheated oven until puffed and golden, 20 to 25 minutes.
