Creating your Peach Cake with Brown Sugar Frosting involves a few straightforward steps:

1. Preheat Your Oven: Preheat your oven to 350°F (175°C) and grease two 9-inch round cake pans.
2. Mix Dry Ingredients: In a bowl, whisk together the flour, baking powder, baking soda, and salt.
3. Cream Butter and Sugar: In another mixing bowl, cream the softened butter and granulated sugar until light and fluffy.
4. Add Eggs and Vanilla: Add the eggs one at a time, beating well after each addition. Then mix in the vanilla extract.
5. Combine Dry Ingredients: Gradually add the dry ingredient mixture to the butter mixture, alternating with the buttermilk until just combined.
6. Fold in Peaches: Gently fold in the chopped peaches until evenly distributed in the batter.
7. Pour into Pans: Divide the batter evenly between the prepared cake pans.
8. Bake: Bake for 30-35 minutes, or until a toothpick inserted in the center comes out clean.
9. Cool the Cakes: Allow the cakes to cool in the pans for about 15-20 minutes, then transfer them to wire racks to cool completely.
10. Prepare Frosting: In a saucepan over medium heat, melt the ½ cup of butter with the brown sugar and milk. Stir until combined and bring to a gentle boil. Remove from heat and let cool slightly.
11. Whip the Frosting: After cooling for a few minutes, whisk in the powdered sugar and vanilla extract until smooth and creamy.
12. Frost the Cakes: Once the cake layers have cooled completely, place one layer on a serving plate. Top with a generous amount of brown sugar frosting. Place the second layer on top and frost the top and sides of the cake.

This will yield a scrumptious Peach Cake with a decadent brown sugar frosting, perfect for any occasion!