Summer never tasted so good.
In a nonstick skillet, melt the butter over medium-high. Add the peaches, brown sugar, and allspice. Cook, stirring occasionally, until the peaches soften, 3 to 5 minutes. Transfer to a plate and let cool. In a large bowl, mix the ice cream with the peaches. Transfer the ice cream to an airtight container and freeze until firm, about 3 hours.
Arrange the racks in the upper and lower thirds of the oven. Preheat the oven to 400°. Line 2 baking sheets with parchment. In a medium bowl, whisk the flour, cream of tartar, baking soda, and salt. In a large bowl, using an electric mixer, beat the butter and 3/4 cup sugar until light and fluffy. Beat in the egg and vanilla. Add the dry ingredients; beat on low speed just to blend.
In a medium bowl, whisk the remaining 2 tbsp. sugar with the cinnamon. Scoop out a rounded tablespoon of dough, roll into a ball, and then coat in the cinnamon sugar. Repeat with the remaining dough. Divide the dough between the baking sheets. Using a flat-bottom glass, flatten the cookies to 1/ 3 to 1/4 inch thick. Bake until the cookies puff up and then begin to fall and the edges are set but the centers are still soft, 9 to 10 minutes. Let the cookies cool on a wire rack.
Scoop 1/ 3 cup of ice cream onto the flat side of 1 cookie. Top with another cookie, flat-side down. Press down to adhere. Repeat with the remaining cookies and ice cream, freezing the ice cream sandwiches as you make them. Freeze until firm, about 4 hours.
This recipe originally appeared in our Summer 2020 issue. Get the magazine here.