Brown your butter: Melt butter in a small/medium saucepan over medium-low heat. It will melt, then foam, then turn clear golden and finally start to turn brown and smell nutty. Stir frequently, scraping up any bits from the bottom as you do. Keep your eyes on it; it burns very quickly after it browns and the very second that you turn around to do something else. Set it in the freezer until solid (about 30 minutes).
[Don’t have time for all this brown butter madness? Check the head notes to use regular softened butter instead.]
Preheat the oven to 375°F (190°C). Butter a 9×13 inch pan, or spray it with a nonstick spray. In a medium bowl, stir together sugar, baking powder, flour, salt and spices with a whisk. Use a pastry blender, fork or your fingertips, blend the solidified brown butter and egg into the flour mixture. It will be crumbly. Pat 3/4 of the crumbs into the bottom of the prepared pan, pressing firmly. Tile peach slices over crumb base in a single layer. Scatter remaining crumbs evenly over peaches and bake in preheated oven for 30 minutes, until top is slightly brown and you can see a little color around the edges. Cool completely in pan before cutting into squares.