Creating the Peach Cake with Brown Sugar Frosting is a straightforward process if you follow these steps carefully:

1. Preheat the Oven: Begin by preheating your oven to 350°F (175°C). Grease and flour two 9-inch round cake pans or line them with parchment paper for easy removal.

2. Mix Dry Ingredients: In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set this mixture aside.

3. Cream Butter and Sugar: In a large bowl, using an electric mixer, cream together the softened butter and granulated sugar until light and fluffy.

4. Incorporate Eggs and Vanilla: Add the eggs one at a time, mixing well after each addition. Then, add the vanilla extract and combine.

5. Add Dry Ingredients: Gradually add the flour mixture to the wet ingredients, alternating with the buttermilk. Mix until just combined; do not overmix.

6. Fold in Peaches: Gently fold in the diced peaches, ensuring they are evenly distributed throughout the batter.

7. Divide Batter: Pour the batter evenly into the prepared cake pans. Use a spatula to smooth the tops.

8. Bake: Place the pans in the preheated oven and bake for 30-35 minutes, or until a toothpick inserted in the center comes out clean.

9. Cool the Cakes: Once baked, remove the pans from the oven and let the cakes cool in the pans for about 20-25 minutes before transferring them to wire racks to cool completely.

10. Prepare the Frosting: In a medium saucepan over medium heat, melt the butter and brown sugar together. Stir until well combined, then bring to a boil. Allow to boil for 1 minute, stirring frequently. Remove from heat and let cool slightly.

11. Mix the Frosting: In a bowl, combine the powdered sugar, milk, and vanilla extract. Gradually add the brown sugar mixture to the powdered sugar mixture, stirring until smooth and creamy.

12. Frost the Cake: Once the cakes are completely cooled, place one layer on a serving plate. Spread a layer of frosting on top, then place the second cake layer on top and frost the top and sides of the cake.