Step 1: Prepare Peach Compote - In a medium saucepan, combine diced yellow peaches, brown sugar, and cornstarch over medium heat. Cook for about 5-7 minutes, stirring gently until the peaches are tender and the mixture thickens. Remove from heat and allow the peach compote to cool fully while you preheat the oven.

Step 2: Preheat Oven - Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.

Step 3: Make Cinnamon Crumble - In a mixing bowl, combine flour, brown sugar, and cinnamon, then drizzle in melted butter. Mix until you form a consistent paste. Refrigerate for about 10-15 minutes, then bake for 5 minutes until lightly golden; cool and crumble.

Step 4: Mix Dry Ingredients - In a separate bowl, whisk together flour, cinnamon, baking powder, baking soda, and a pinch of salt.

Step 5: Mix Wet Ingredients - In a large mixing bowl, whisk together melted butter, granulated sugar, and brown sugar until smooth. Add the egg and mix until combined.

Step 6: Combine Mixtures - Gently fold dry mixture into wet mixture until just combined; a few lumps are okay.

Step 7: Scoop and Bake Cookies - Drop heaping tablespoons of dough onto the prepared baking sheet, spacing them about 2 inches apart. Bake for 11-12 minutes until the edges are set.

Step 8: Prepare Cream Cheese Frosting - Beat softened cream cheese, powdered sugar, cinnamon, and vanilla extract until smooth and creamy.

Step 9: Assemble Cookies - Once cookies are cool, spoon peach compote into indentations, pipe frosting on top, and sprinkle with crumble.