Follow these steps carefully to create your perfect Peach Cake with Brown Sugar Frosting:

1. Preheat Oven: Preheat your oven to 350°F (175°C). Grease and flour two 9-inch round cake pans.
2. Mix Dry Ingredients: In a large bowl, whisk together the flour, baking powder, baking soda, and salt.
3. Cream Butter and Sugar: In a separate bowl, cream the softened butter and granulated sugar until light and fluffy.
4. Add Eggs and Vanilla: Beat in the eggs, one at a time, followed by the vanilla extract, mixing well.
5. Combine Mixtures: Gradually add the dry ingredients to the wet mixture, alternating with the buttermilk. Mix until smooth.
6. Fold in Peaches: Gently fold in the diced peaches until evenly distributed throughout the batter.
7. Divide Batter: Pour the batter evenly into the prepared cake pans.
8. Bake: Bake in the preheated oven for 30-40 minutes, or until a toothpick inserted in the center comes out clean.
9. Cool Cakes: Remove from the oven and allow the cakes to cool in the pans for 15 minutes. Then, transfer them to wire racks to cool completely.
10. Make Frosting: In a bowl, beat together brown sugar and butter for the frosting until smooth. Add powdered sugar, milk, and vanilla, beating until creamy.
11. Frost the Cake: Once the cakes have cooled, spread frosting between the layers and over the top and sides of the cake.

Following these steps will result in a stunning Peach Cake with Brown Sugar Frosting that is sure to delight!