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

In a medium bowl, whisk together the flour, baking powder, baking soda, salt, and cinnamon. Set aside.

In a large bowl, cream together the softened butter, granulated sugar, and brown sugar until light and fluffy. Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.

Gradually add the flour mixture to the butter mixture, alternating with the buttermilk. Begin and end with the flour mixture. Mix until just combined. Gently fold in the diced peaches.

Pour the batter into the prepared baking pan and spread it evenly. Bake for 30-35 minutes, or until a toothpick inserted in the center comes out clean. Allow the cake to cool in the pan for about 15 minutes, then transfer to a wire rack to cool completely.

While the cake is cooling, prepare the frosting. In a saucepan over medium heat, melt the butter and brown sugar together, stirring until smooth. Add the milk and bring to a boil. Remove from heat and let cool for about 10 minutes.

Once cooled, gradually whisk in the powdered sugar and vanilla extract until smooth and creamy.

Spread the brown sugar frosting over the cooled peach cake. Slice and serve.