In a mixing bowl, beat the softened unsalted butter with an electric mixer on medium speed until creamy and smooth, about 2 minutes.
Gradually add the powdered sugar, one cup at a time, mixing well after each addition until fully combined. The mixture will be thick.
Add the peppermint extract, vanilla extract, and 2 tablespoons of milk. Continue to mix until the ingredients are well incorporated. If the dough is too stiff, add an additional tablespoon of milk and mix again until achieving a soft dough consistency.
If desired, add a few drops of red food coloring to create a marbled effect. Gently fold the color into the dough using a rubber spatula.
Dust a clean work surface with powdered sugar and turn the dough out onto it. Roll the dough into small balls, about 1 inch in diameter, and then flatten them slightly to form disks.
Line a baking sheet with parchment paper and place the mints on it. Allow to air dry at room temperature for at least 2 hours, or until they are firm to the touch.
Once dried, store the mints in an airtight container at room temperature for up to two weeks.