Preheat your oven to 350°F (175°C) and grease a 9x13-inch baking pan.

In a medium bowl, whisk together flour, baking powder, baking soda, and salt until well combined.

In a large mixing bowl, cream together the softened butter and sugar using a mixer until light and fluffy.

Add the eggs one at a time, then mix in vanilla extract and sour cream until smooth.

Combine the dry ingredients into the wet mixture gently, then fold in the diced peaches.

Pour the batter into the greased pan and bake for 30-35 minutes until a toothpick comes out clean.

Allow the cake to cool in the pan for 15 minutes, then transfer to a wire rack to cool completely.

In a saucepan, melt butter over medium heat, stir in brown sugar, and cook until smooth.

Remove from heat, mix in milk and bring to a boil, then let it cool slightly before whisking in powdered sugar.

Frost the cooled cake with the brown sugar frosting and allow to set before slicing.