Preheat your oven to 350°F (175°C). Grease and flour a 9-inch round cake pan to prevent sticking.

In a large mixing bowl, cream together the softened butter, brown sugar, and granulated sugar using a whisk or electric mixer until light and fluffy. This process incorporates air into the mixture, which helps the cake rise.

Add the eggs one at a time, mixing well after each addition. This ensures even distribution of the eggs throughout the batter.

In another bowl, whisk together the sifted flour, baking powder, baking soda, and salt. This helps to evenly distribute the leavening agents.

Gradually add the dry ingredients to the wet mixture, alternating with the buttermilk and vanilla extract. Start and end with the dry ingredients. Mix until just combined; overmixing can lead to a dense cake.

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

Pour the batter into the prepared cake pan, smoothing the top with a spatula.

In a small bowl, combine the topping ingredients: brown sugar, cinnamon, and melted butter. Sprinkle this mixture evenly over the top of the batter.

Bake in the preheated oven for 40-45 minutes, or until a toothpick inserted into the center comes out clean. This ensures that the cake is fully cooked.

Once baked, remove the cake from the oven and let it cool in the pan for 10 minutes before transferring it to a cooling rack to cool completely.

Once cooled, slice the cake into wedges and serve. This cake is delicious on its own or can be paired with whipped cream or vanilla ice cream.