Whisk the cookie mix and flour together in a medium bowl. Prepare the cookie dough according to the package directions for drop cookies. Divide the dough into 2 pieces and flatten into discs. Wrap each disc in plastic wrap and chill for 30 minutes.
Position oven racks in the top and bottom thirds of the oven and preheat to 350 degrees F. Spray two 10-inch ovensafe rimmed plates with nonstick cooking spray and dust with flour; set aside.
Put one dough disc on a 12-inch-long piece of parchment and use a rolling pin to roll it to fit one of the plates. Gently place the plate face-down on the dough and trim any excess dough. Slide your hand under the parchment and, with your other hand holding the plate, flip it so the dough is now on the plate. Center the dough on the plate and peel off the parchment. Working from the center of the plate, gently press the dough down with the bottom of a 1/4-cup metal measuring cup to push out any air below the dough. Repeat with the second piece of dough and plate.
Place each plate on a baking sheet and bake until the cookie plates are slightly golden, about 12 minutes. Carefully remove from the oven and press the middle of the cookie plates again with the measuring cup to flatten. Place 1 peppermint candy in the center of each cookie plate and surround with 6 more candies. Use the remaining candies to line the circumference of the outer rim of the plates, placing them 1/4 inch inside the rim and leaving 1/8 inch between them so they can melt together.
Place back in the oven, switching the positions of the baking sheets, and bake until the outer rims of the cookie plates are golden brown and the centers have just started to barely brown, about 4 minutes.
Transfer to a cooling rack to cool 5 minutes. Run a paring knife between the outer rims of the plates and the cookie plates to help release the cookie plates while they cool. Cool completely at room temperature, about 2 1/2 hours. Carefully remove the cookie plates. Serve topped with your favorite holiday cookies.
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