Preheat your oven to 350°F (175°C). Grease and flour two 9-inch round cake pans and line the bottoms with parchment paper to prevent sticking.

In a large mixing bowl, whisk together the flour, 3/4 cup of granulated sugar, baking powder, baking soda, and salt. This ensures even distribution of the leavening agents.

In another bowl, cream together the softened butter and the remaining 1/4 cup of granulated sugar using an electric mixer on medium speed until light and fluffy, about 3-4 minutes.

Add the eggs one at a time, mixing well after each addition. Then mix in the vanilla extract.

Gradually add the dry ingredients to the butter mixture, alternating with the buttermilk. Start and end with the dry ingredients. Mix until just combined; do not overmix to keep the cake light and fluffy.

Gently fold in the diced peaches with a rubber spatula, being careful not to break them up too much.

Divide the batter evenly between the prepared cake pans. Smooth the tops with a spatula.

Bake in the preheated oven for 30-35 minutes, or until a toothpick inserted in the center comes out clean. Allow the cakes to cool in the pans for 10 minutes before transferring to a wire rack to cool completely.

In a medium mixing bowl, beat the softened butter and brown sugar together until well combined and creamy, about 2-3 minutes.

Add the heavy cream and vanilla extract, mixing until smooth.

Gradually add the sifted powdered sugar, mixing on low speed until combined, then increase to medium speed and beat until fluffy and spreadable, about 2-3 minutes.

Once the cakes are completely cool, place one layer on a serving plate. Spread a generous amount of brown sugar frosting on top.

Place the second layer on top and frost the top and sides of the cake with the remaining frosting. Use a spatula to create a smooth finish or decorative swirls.

Slice and serve. Enjoy your delicious peach cake with brown sugar frosting!