Preheat the oven and prep the pans. Position a rack in the center of the oven and preheat the oven to 350°F. Line two half sheet pans with parchment paper.
Mix the dry ingredients. In a medium bowl, whisk together the flour, baking soda, and salt.
Mix the wet ingredients. In a small liquid measuring cup, whisk together the milk, vanilla, and food coloring.
Cream the butter and sugar, then add the egg. In the bowl of a stand mixer fitted with the paddle attachment, combine the butter and sugar. Beat on medium-high until light, fluffy, and doubled in volume, 2 to 3 minutes, using a rubber spatula to scrape down the bottom and sides of the bowl as necessary. Reduce the mixer to low, add the egg, and beat until just combined.
Alternate adding the dry and wet ingredients in two parts. With the mixer on low, add half of the dry ingredients and beat until just combined. Scrape down the bottom and sides of the bowl, and with the mixer on low, add half the wet ingredients. Repeat until both the remaining halves of the dry and wet ingredients are just combined.
Assemble the cookies. Place the cookie crumbs in a medium, shallow bowl. Use a 1-tablespoon cookie dough scoop to portion the cookie dough into balls. Dip the bottom of each cookie dough ball into the cookie crumbs to coat its bottom. Place the cookie dough balls at least 3 inches apart on the prepared sheet pans. Bake the cookies. Bake one pan at a time for 10 minutes, or until the edges have set but the centers are still soft.
Finish assembling the cookies. Place the pan on a wire rack and immediately press a HERSHEY’S KISSES Candy Cane Mint Chocolate into the center of each cookie. Cool the cookies completely on their pans on the wire racks. Serve and store. Serve warm, or at room temperature. The cookies can be stored in an airtight container or zip-top bag at room temperature for up to 3 days.