Preheat oven to 350 degrees. Grease a 9-inch cake pan or a deep dish pie pan. and line with parchment paper. Line the bottom of the pan with sliced peaches, arranging them in concentric circles. Mix ¼ cup melted butter and ⅓ cup brown sugar in a small bowl and pour over the peaches. Set aside.
Add softened butter and granulated sugar to bowl of a stand mixer. Beat together with paddle attachment until light and fluffy, about 4 minutes. Add one egg, beat, add other egg, beat, and then add vanilla extract and almond extract and beat.
In a separate bowl, whisk flour, baking powder, and salt. Add half of the dry ingredients to the bowl of the stand mixer and beat just until combined. Add milk and beat just until combined. Finally, add last of dry ingredients and beat just until combined.
Gently pour batter over the peaches, being careful not to slide them around. Spread into an even layer. Bake cake in preheated oven for 30 minutes. After 30 minutes, loosely cover with foil to prevent cake from browning too much. Cook for another 10-15 minutes, or until toothpick comes out clean when inserted in the center.
Remove from oven and let cool for 10 minutes. Then, flip cake onto plate to finish cooling or serve warm with ice cream. The remaining can be frozen for up to 3 months.