Follow these easy steps to create the exquisite Peach Cake with Brown Sugar Frosting:

1. Preheat the Oven: Preheat your oven to 350°F (175°C). Grease and flour two 9-inch round cake pans.

2. Mix Dry Ingredients: In a large bowl, whisk together the flour, granulated sugar, brown sugar, baking powder, baking soda, salt, cinnamon, and nutmeg.

3. Cream Butter: In a separate bowl, combine the softened butter and sugar mixture, creaming them until light and fluffy.

4. Add Eggs and Vanilla: Gradually add the eggs, one at a time, mixing well after each addition. Stir in the vanilla extract.

5. Incorporate Sour Cream: Mix in the sour cream until combined, creating a smooth batter.

6. Fold in Peaches: Gently fold in the diced peaches, ensuring even distribution throughout the batter.

7. Transfer to Pans: Divide the batter evenly between the prepared cake pans, smoothing the top with a spatula.

8. Bake: Place in the preheated oven and bake for 35-40 minutes or until a toothpick inserted in the center comes out clean.

9. Cool the Cakes: Once baked, let the cakes cool in their pans for about 10 minutes before transferring them to wire racks to cool completely.

10. Prepare the Frosting: In a saucepan over medium heat, combine the butter and brown sugar. Stir until melted and combined, then add the milk and bring to a boil for 2 minutes.

11. Cool the Frosting: Remove from heat, let it cool slightly, then gradually whisk in the powdered sugar and vanilla extract until smooth and spreading consistency is achieved.

12. Frost the Cake: Once the cake layers are cool, place one layer on a serving platter. Spread frosting on the top, then gently place the second layer on top. Finish by frosting the top and sides of the cake.