Preheat oven to 375 degrees. Grease and flour a standard 12 cup muffin pan.
Brown butter: Heat butter gently in a pot over low heat until completely melted. Increase heat to medium, and continue to cook, stirring frequently to prevent burning. The butter is ready when it has a nutty/toasty smell and a deep brown color; about 7-8 minutes of cooking. More in-depth info on browning butter here. Remove browned butter from heat and set aside to cool slightly.
In a medium bowl, stir together the flour, baking powder, and salt.
In a larger bowl, mix the brown butter, sugar, and brown sugar together until smooth. Stir in the eggs, followed by the yogurt and almond extract until everything is well combined. Fold in the flour mixture until fully incorporated.
Divide batter evenly between the 12 muffin wells.
Slice the almond paste into 12 equal pieces, shaping each into a small disk about ¾” in diameter. Press one almond paste disk into the center of each batter-filled muffin well (this will form a delicious almond-y core for each cake).
Top each cake with a couple of peach slices and about 1 tsp sliced almonds. Bake cakes until golden almonds on top are beginning to brown and cakes are puffed and golden, about 25 minutes.
Let cakes rest for about 5 minutes, then run a knife around each cake and pop out of the muffin pan. Cool cakes on a wire rack.