Preheat Oven and Prepare Baking Sheet:
Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper or a silicone baking mat.
Make the Crumble Topping:
In a small bowl, combine the flour, brown sugar, and cinnamon. Add the cold, cubed butter and use your fingers or a fork to mix until the mixture resembles coarse crumbs. Set aside.
Prepare the Cookie Dough:
In a large mixing bowl, cream the butter, granulated sugar, and brown sugar together until light and fluffy. Add the egg and vanilla extract, mixing until combined.
In another bowl, whisk together the flour, baking soda, salt, and cinnamon. Gradually add the dry ingredients to the wet ingredients, mixing just until combined.
Gently fold in the diced peaches.
Shape the Cookies:
Scoop tablespoon-sized portions of dough onto the prepared baking sheet, spacing them about 2 inches apart. Gently press each cookie down slightly to flatten.
Add the Crumble Topping:
Sprinkle a small amount of the crumble topping onto each cookie, pressing it lightly into the dough to adhere.
Bake:
Bake the cookies for 12–14 minutes, or until the edges are lightly golden. Allow them to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.
Serve and Enjoy:
Serve these cookies warm or at room temperature, and enjoy the comforting flavors of peach cobbler in every bite!