Step 1

Preheat oven to 425°F with racks in middle and lower third positions. Line bottom of an 8-inch square baking pan with parchment paper. Grease parchment paper and sides of pan with butter. Sprinkle bottom of prepared pan with 3 tablespoons sugar. Line bottom of pan with overlapping peach slices in alternating rows. Sprinkle peaches with 1 tablespoon sugar. Set aside.

Step 2

Sift together flour, baking powder, and salt in a bowl; set aside. Beat butter and remaining 2/3 cup sugar with a stand mixer fitted with the paddle attachment on medium-high speed until light and fluffy, about 5 minutes, stopping to scrape down sides as needed. With mixer running on low speed, add almond meal and vanilla, beating until just combined, about 1 minute. Add flour mixture and milk alternately to butter mixture, beginning and ending with flour mixture, beating on low speed until fully combined after each addition. Spoon batter over peaches, and smooth top using a spatula.

Step 3

Bake on lower rack in preheated oven 10 minutes. Reduce oven temperature to 350°F, and immediately transfer cake to middle rack. Bake until a wooden pick inserted in center of cake comes out clean, about 25 minutes. Transfer cake to a wire rack, and let cool in pan 20 minutes. Invert cake onto a platter, and let cool completely, about 30 minutes. Slice cake, and serve with vegan whipped topping or ice cream, if desired.