Start by preheating your oven to 400°F. While it heats, measure out all your ingredients and have them ready at your work station. Sift the powdered sugar into a small bowl to remove any lumps—this ensures a smooth, lump-free glaze later. Finely crush the starlight mint candies into small pieces (I use the back of a measuring cup for even crushing) and set aside. This prep work takes just a few minutes but sets you up for smooth, uninterrupted baking.
In a large mixing bowl, combine the softened butter and sugar, beating until the mixture is light, fluffy, and pale—this usually takes about 2-3 minutes with an electric mixer. This creaming process incorporates air into the dough, which helps the cookies spread and bake evenly. Add the room-temperature egg, vanilla extract, and peppermint flavoring, beating until everything is fully combined and smooth. The room-temperature egg incorporates more smoothly into the butter mixture, creating a better emulsion.
In a separate bowl, whisk together the flour and salt. Add the dry mixture to the wet ingredients from Step 2 and beat on low speed until just combined—stop as soon as no streaks of flour remain. Overmixing at this stage can toughen the cookies, so resist the urge to keep beating once everything is incorporated. If the dough feels too soft to hold a shape in the cookie press, cover it and refrigerate for 1 hour. The dough should be firm enough to pipe but still pliable.
Transfer the dough from Step 3 into a cookie press fitted with your desired decorative plate. Line baking sheets with parchment paper and pipe cookies directly onto the sheets, leaving about 1 inch between each cookie. Slide the sheets into your preheated 400°F oven and bake for 5-6 minutes—the cookies should be set but still pale, with perhaps the tiniest hint of browning on the bottoms. These delicate spritz cookies bake quickly, so keep a close eye on them.
As soon as the cookies come out of the oven, transfer them to cooling racks to cool completely. While they cool, prepare the glaze by whisking together the sifted powdered sugar from Step 1 with 1-2 tablespoons of milk, starting with 1 tablespoon and adding more until you reach a consistency that drizzles easily but still holds its shape on the cookie. The glaze should be thin enough to flow smoothly but thick enough to not pool at the base of the cookies.
Once the cookies are completely cooled, drizzle the glaze from Step 5 over each cookie using a fork, small spoon, or squeeze bottle—I prefer a small squeeze bottle for the most control. Immediately sprinkle each glazed cookie with a few pieces of the crushed starlight mint candies from Step 1, as the glaze sets quickly and the candies will stick better while it's still wet. Let the glaze set for about 10-15 minutes before serving or storing.