Preheat oven to 350°F (175°C) and grease a 9-inch round cake pan.
Cream the softened butter and 3/4 cup of the brown sugar in a large bowl until light and fluffy.
Beat in the eggs one at a time, followed by the vanilla extract.
Whisk together flour, baking powder, and salt in a separate bowl.
Gradually add dry ingredients to the butter mixture, alternating with milk, beginning and ending with dry ingredients.
Pour batter into the prepared pan and smooth the top.
Toss peach slices with remaining 1/4 cup brown sugar and cinnamon.
Arrange peach slices on top of the batter in a circular pattern.
Bake for 45 minutes, or until a toothpick inserted into the center of the cake comes out clean.
Cool in the pan for 10 minutes before transferring to a wire rack to cool completely.