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

In a medium bowl, whisk together 1 1/2 cups of flour, baking powder, baking soda, and salt. Set aside.

In a large bowl, beat together the room temperature butter and granulated sugar until light and fluffy. Add eggs one at a time, beating well after each addition. Mix in the vanilla extract.

Gradually add the dry ingredients to the butter mixture, alternating with the sour cream, beginning and ending with the dry ingredients. Mix just until combined.

Gently fold in the sliced peaches. Pour the batter into the prepared baking dish, spreading it evenly.

Prepare the crumb topping: In a medium bowl, mix together the remaining 1/2 cup of flour, brown sugar, cold butter cubes, and ground cinnamon. Use a pastry cutter or your fingers to blend the mixture until it resembles coarse crumbs.

Sprinkle the crumb topping evenly over the cake batter.

Bake in the preheated oven for 40 minutes, or until a toothpick inserted into the center comes out clean.

Allow the cake to cool in the pan on a wire rack before serving.