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, and salt. Set aside.
In a large mixing bowl, cream the softened butter and brown sugar together until light and fluffy, about 3-4 minutes.
Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.
Gradually add the dry ingredients to the wet mixture, alternating with the sour cream. Begin and end with the flour mixture, mixing until just combined.
Gently fold in the diced peaches and cinnamon until evenly distributed.
Pour the batter into the prepared baking pan and spread it evenly. Sprinkle the tablespoon of sugar over the top for added sweetness and crunch.
Bake for 35-40 minutes, or until a toothpick inserted in the center comes out clean.
Allow the cake to cool in the pan for about 10 minutes before transferring it to a wire rack to cool completely.