**Preheat the Oven:** Preheat your oven to 350°F (175°C) and grease or line a 9x9-inch baking pan with parchment paper.
**Make the Crumb Topping:** In a bowl, combine the flour, granulated sugar, brown sugar, and cinnamon. Add the melted butter and mix until crumbly. Set aside.
**Prepare the Cake Batter:** In a large mixing bowl, cream the softened butter and granulated sugar until light and fluffy. Beat in the eggs, one at a time, followed by the vanilla extract.
**Combine Dry Ingredients:** In a separate bowl, whisk together the flour, baking powder, baking soda, and salt.
**Mix the Batter:** Gradually add the dry ingredients to the wet mixture, alternating with the sour cream, beginning and ending with the dry ingredients. Mix until just combined.
**Assemble the Cake:** Spread the batter evenly into the prepared pan. Top with the chopped peaches, gently pressing them into the batter. Sprinkle the crumb topping evenly over the peaches.
**Bake:** Bake for 40-45 minutes or until a toothpick inserted into the center comes out clean.
**Cool and Serve:** Allow the cake to cool in the pan for 15 minutes before transferring to a wire rack to cool completely. Serve warm or at room temperature.