Pour melted butter into an 8”or 9” cake pan and swirl to coat the bottom. Sprinkle evenly with ½ cup light brown sugar. Arrange the peach slices on top of the brown sugar, starting the middle and working towards the edge, until the bottom of the cake pan is filled. Discard any extra slices.
In the bowl of an electric mixer fitted with the paddle attachment, beat together the softened butter and remaining light brown sugar until light and fluffy, scraping down the sides of the bowl as needed. Add the egg and beat until well incorporated. Add the applesauce and vanilla and mix until uniform.
In a separate bowl, whisk together the flour, baking powder and salt.
Alternate adding the flour mixture and the milk into the mixer bowl, fully incorporating each addition before adding the next. Begin and end with the flour mixture, scraping the bowl between additions.
Pour the cake batter into the prepared pan and gently spread with a spatula to cover the peaches completely. Gently tap the cake pan a few times on a hard surface, like the counter, to allow the cake mixture to work into the spaces between the peaches and the air bubbles to come out.
Bake for 40-45 minutes, until the top is slightly browned and a toothpick inserted into the center comes out clean. Remove from oven and allow the cake to cool in the pan for 10 minutes.
Gently run a knife along the edge of the cake to help it release from the pan. Place the serving plate you wish to use on top of the cake pan. Flip the pan over and allow the cake to release onto the serving plate.