Prepare Peach Compote: In a medium saucepan, combine diced yellow peaches, brown sugar, and cornstarch. Cook over medium heat for about 5–7 minutes, stirring constantly, until the peaches become tender and the mixture thickens. Once ready, remove from heat and allow the peach compote to cool completely before using it as a topping for your Peach Cobbler Cookies.

Make Cinnamon Crumble: In a mixing bowl, whisk together flour, brown sugar, and ground cinnamon. Pour in melted unsalted butter, mixing until a crumbly paste forms. Chill the mixture for about 10 minutes, then spread it out on a baking sheet. Bake in a preheated oven at 350°F (175°C) for 5 minutes until lightly golden, then cool before breaking into crumbly pieces.

Prepare Cookie Dough: In a large bowl, combine the dry ingredients: flour, baking powder, baking soda, ground cinnamon, and a pinch of salt. In another bowl, whisk together melted butter, granulated sugar, brown sugar, egg, and vanilla extract until smooth. Gradually fold the dry mixture into the wet ingredients, blending just until combined.

Form Cookies: Using a cookie scoop, drop rounded tablespoons of dough onto a parchment-lined baking sheet, spacing them 2 inches apart. Preheat the oven to 350°F (175°C) and bake for 11-12 minutes, until the cookies are puffy and lightly golden around the edges. Make an indentation in the center of each cookie using your thumb.

Make Frosting: In a medium mixing bowl, beat softened cream cheese, powdered sugar, ground cinnamon, and vanilla extract until smooth and creamy. Transfer the frosting into a piping bag fitted with a decorative tip, making it easy to pipe onto your baked cookies.

Assemble Cookies: Fill each indentation with the prepared peach compote, topping it off with a swirl of the cinnamon cream cheese frosting. Sprinkle the buttery crumble over each cookie.