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.

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 a stand mixer fitted with a paddle attachment, mix the cold butter on medium-high speed until it forms a large clump, 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 the bowl. Slowly add in the 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, creating a wide well.

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

Preheat oven to 375°F. Bake cookies until light golden brown, about 12-15 minutes. 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 ½ tablespoon cooled peach topping into the thumbprint of each cookie.

Drizzle with glaze and sprinkle with cookie crumble, then finish with another small drizzle.