Step 1: In a large mixing bowl, place ½ cup (1 stick) unsalted butter, softened to room temperature. Beat the butter with an electric mixer until it's light, fluffy, and very creamy, which usually takes about 1-2 minutes.
Step 2: Gradually add 3 ½ cups powdered sugar to the creamed butter, about ½ cup at a time. Mix thoroughly after each addition until the sugar is fully incorporated and the mixture forms a thick, somewhat crumbly dough.
Step 3: Stir in 1 teaspoon vanilla extract and 1 tablespoon milk. Continue mixing until the dough is smooth and uniform.
Step 4: Add 1-2 tablespoons peppermint extract. Start with 1 tablespoon, mix, and taste. If you desire a stronger minty kick, add the second tablespoon gradually.
Step 5: If you want to add a pop of color, incorporate a few drops of your desired food coloring. Mix until the color is evenly distributed throughout the dough.
Step 6: Roll small portions of the mint mixture into bite-sized balls, roughly the size of a marble. Place these onto a parchment-lined baking sheet.
Step 7: For classic flat mints, gently press each ball with the back of a fork to create a crisscross pattern. Alternatively, you can press the entire mixture into a shallow square pan, then cut into small squares, or use candy molds.
Step 8: Refrigerate the shaped mints for at least 30 minutes, or until they are firm to the touch.
Step 9: Once firm, transfer your butter mints to an airtight container. Store them in the refrigerator for up to 2 weeks. They also freeze beautifully for up to 3 months; just thaw at room temperature for a few minutes before enjoying.