Add peaches to a medium saucepan with sugar, cinnamon, nutmeg, salt, and lemon juice. Heat over medium heat and cook until peaches reduce in size and the liquid thickens, about 10 minutes.

In a small bowl, mix together cornstarch and water to create a slurry, then stir into the peaches and let come to a boil. Stir and cook for an additional 2 minutes. Remove from the heat and let cool to room temperature. Set aside until ready for use.

Line two sheet pans with parchment paper.

In a medium bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, and nutmeg. Set aside.

In the bowl of your stand mixer fitted with paddle attachment, mix the cold butter on medium high speed until it comes mostly together as a large clump around the paddle, about 1 minute. Add in both sugars and beat for an additional 2 minutes.

Reduce speed to low and add eggs and vanilla extract. Scrape down sides and bottom of bowl. Slowly add in flour mixture, mixing until flour is incorporated.

Using a #16 scoop (4 tablespoons), scoop out 12 cookies and evenly space 6 cookies on each prepared sheet pan. Gently press your thumb into the center of each cookie making sure not to go down too far, just going halfway down and wiggling around to create a wide well.

Place pans in the refrigerator to chill for 30-35 minutes.

Preheat oven to 375F. Bake cookies until light golden brown, about 12-15 minutes. (Do not overbake. The dough will look slightly under baked in the center, where your thumbprint is, but will continue to set up as it cools.)

Cool slightly on a wire rack, about 5 minutes.

Whisk together glaze ingredients in a small bowl until smooth.

Take one cookie and crumble into small bits.

Spoon about 1 ? tablespoon cooled peach topping into the thumbprint of each cookie.

Drizzle with glaze and sprinkle with cookie crumble, then finish with another small drizzle and enjoy. Best served immediately after assembling.