In a medium saucepan, add peaches, sugar, cinnamon, nutmeg, salt, and lemon juice. Heat over medium heat for about 10 minutes until peaches reduce and liquid thickens.

In a small bowl, mix cornstarch and water to create a slurry, then stir into the peaches and let come to a boil. Cook for an additional 2 minutes. Remove from heat and let cool to room temperature.

Line two sheet pans with parchment paper.

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

In the stand mixer fitted with the paddle attachment, mix cold butter on medium-high speed until it forms a large clump. Add both sugars and beat for 2 minutes.

Reduce speed to low and add eggs and vanilla extract. Scrape bowl and slowly add flour mixture, mixing until incorporated.

Scoop out 12 cookies using a #16 scoop (4 tablespoons) and space 6 cookies on each prepared sheet pan. Press your thumb into the center of each cookie to create a well.

Chill the pans in the refrigerator for 30-35 minutes.

Preheat oven to 375°F. Bake cookies for 12-15 minutes until light golden brown.

Cool cookies slightly on a wire rack for about 5 minutes.

In a small bowl, whisk together glaze ingredients until smooth.

Take one cookie and crumble into small bits. Spoon about 1 ½ tablespoons of cooled peach topping into each cookie's thumbprint. Drizzle with glaze and sprinkle with cookie crumble.