• Preheat the oven to 350 degrees F. Line baking sheets with parchment paper.

Crumble Topping

• Combine 3/4 cup all-purpose flour, 1/2 cup dark brown sugar, 1/2 teaspoon cinnamon, 1/4 teaspoon salt, and 5 tablespoons unsalted butter, melted in a medium bowl. Stir with a fork until the mixture looks like wet sand and small crumbs form. Spread it onto a parchment-lined baking sheet and bake for 10 minutes, or until golden. Cool completely, then break apart any large pieces with a fork or clean hands. Cooling keeps the crumble crisp.

Cinnamon Sugar Topping

• Combine 1/4 cup granulated sugar and 1/2 teaspoon cinnamon in a shallow bowl.

Peach Cobbler Filling

• Combine 4 cups diced peaches, 1/2 cup dark brown sugar, 1 tablespoon granulated sugar, 1/2 teaspoon cinnamon, and 1/4 teaspoon nutmeg in a medium saucepan over medium heat. Bring to a gentle boil, then reduce the heat and simmer for about 10 minutes, until the peaches soften but still hold their shape.
• In a small bowl, whisk 1 tablespoon cornstarch and 1 tablespoon water into a smooth slurry. Stir it into the peaches and cook until the filling thickens, about 3 to 5 minutes. Remove from the heat, stir in 1 tablespoon vanilla extract, and cool completely.

Cookies

• Make the cookie dough. In a medium bowl, whisk together 4 1/2 cups all-purpose flour, 1/2 teaspoon baking soda, 1 teaspoon baking powder, 1 tablespoon cinnamon, and 1 teaspoon salt.
• In a larger bowl, cream 1 1/2 cups unsalted butter, room temperature, 1 1/2 cups granulated sugar, and 1/2 cup dark brown sugar until light and fluffy. Add 3 large eggs, room temperature and 1 tablespoon vanilla extract and mix until fully combined. Add the dry ingredients and mix until a dough forms.
• Portion the dough into 3-ounce balls, about a third of a cup each. Roll each ball in the cinnamon sugar, place on the prepared baking sheets, and flatten slightly.
• Bake for 14 minutes. Right after removing the cookies from the oven, use the bottom of a quarter-cup measuring cup or the back of a spoon to press a well into the center of each cookie. Pressing the wells while the cookies are warm gives the cleanest results. Cool completely.

Vanilla Glaze

• Combine 1/3 cup powdered sugar and 1/2 teaspoon vanilla extract in a small bowl. Stir in 1 tablespoon of milk until smooth, then add more milk a little at a time until the glaze is pourable, thin enough to drizzle but thick enough to hold its shape.
• Fill each cooled cookie well with the cooled peach filling. Top with the crumble and finish with a drizzle of vanilla glaze. Serve, or store as directed.