Prepare oven and pans. Position a rack in the center of your oven and preheat oven to 350°F. Grease or butter a 10-inch pie pan or 9-inch deep-dish pie pan. This cake would also work in a 9- or 10-inch springform or cake pan.
Combine dry ingredients. Whisk flour, baking powder and salt together in a small bowl. In a larger bowl, beat butter and 1 cup sugar until pale and fluffy with an electric mixer, about 3 minutes. Mix in egg, milk and vanilla until just combined. Add dry mixture gradually, mixing until just smooth.
Combine wet ingredients. In a larger bowl, beat butter and 1 cup sugar until pale and fluffy with an electric mixer, about 3 minutes. Mix in egg, milk and vanilla until just combined.
Combine wet and dry ingredients. Add dry mixture gradually to the wet mixture with mixer on low, mixing until just smooth and flour is just incorporated. Do not overmix.
Add to pan and add peaches. Pour into prepared pie plate. Arrange peaches on top of batter, as closely as possible in a single layer. (Feel free to overlap if needed. You won’t be disappointed.) Sprinkle remaining 2 tablespoons sugar over peaches.
Bake the cake. Bake cake for 10 minutes then reduce oven temperature to 325°F and bake cake until golden brown and a tester comes out free of wet batter, about 50 minutes to 60 minutes. Let cool in pan on a rack. Cut into wedges. Serve with lightly whipped cream.