In a medium saucepan, combine the diced peaches, granulated sugar, light brown sugar, lemon juice, cinnamon, and nutmeg.

Cook over medium heat for 6 minutes or until the peaches begin to soften.

In a small bowl, stir together the cornstarch and water, then add it to the pan.

Cook for another minute until the filling thickens. Remove from heat and stir in the vanilla extract. Let it cool in the fridge.

In a large mixing bowl, cream the softened butter with both sugars until light and fluffy.

Add eggs and vanilla extract, mixing until combined.

Gradually incorporate the flour, baking soda, baking powder, cinnamon, nutmeg, and salt.

Mix until the dough has formed. Chill the dough in the refrigerator for 30 minutes.

After chilling, use a cookie scoop to form the dough into balls. You can chill them further in the fridge or freeze them for future baking.

In a bowl, mix melted butter with the crumble ingredients: light brown sugar, granulated sugar, flour, and cinnamon.

Spread the mixture on a baking sheet covered with parchment paper, and bake at 350°F for about 10-12 minutes, or until golden brown. Allow to cool.

Preheat the oven to 350°F.

Roll the chilled dough balls in a mixture of granulated sugar, cinnamon, and nutmeg.

Place them on prepared cookie sheets, leaving space in between.

Bake for 11-13 minutes. When cookies are removed from the oven, use a round cookie cutter to shape them while they are still warm.

For an added touch of sweetness, mix powdered sugar with vanilla extract, a pinch of cinnamon, and milk to achieve your desired glaze consistency.

Once the cookies have cooled, spoon the chilled peach filling on top of each cookie, sprinkle with the crumble mixture, and drizzle with the prepared glaze.

Serve immediately, and store any leftovers in the fridge.