In a large bowl, add the ½ cup butter. Beat with a hand mixer on medium speed, beat until smooth and creamy.
Gradually add in the 4 cups powdered sugar, beat on low until the powdered sugar is well incorporated into the butter. It won’t come together into a dough yet.
Add in the 1 tablespoon half-and-half or whole milk, 1 teaspoon vanilla extract, and ½ teaspoon peppermint extract. Mix on low until most of mixture begins clumping, then turn the mixer to medium speed and beat until well combined.
Divide the dough into 3 equal portions if you are coloring.
Wrap each portion tightly in plastic wrap and chill for 30 minutes in the fridge.
Remove one portion at a time and add 5 to 7 drops of gel food coloring and work it into the butter mint dough by kneading it until no white streaks are left. If you want a deeper color, add additional drops of gel food coloring and continue kneading it until you reach the desired color.
Rewrap the portion of butter mint dough with plastic wrap and chill for at least 1 hour. Repeat with each portion.
Line baking sheets with parchment paper or silicone mats.
Using a 1 teaspoon measuring spoon or cookie scoop, scoop each butter mint and roll into a ball.
Flatten each ball slightly with your thumb and then using a fork make a slight impression.
Place each mint on the prepared baking sheet. They can be close together as they’re just drying.
Allow the mints to dry at room temperature for 12 to 24 hours.
Store in airtight container at room temperature.
Notes
Storage: Once the mints are dried, store them in an airtight container at room temperature. You can also use a sealed storage bag if you would prefer. The mints can be stored for at least 3 weeks.Freezing: You can also freeze the butter mints if you would prefer. Freeze for up to 3 months in a freezer-safe bag or container. Then thaw on the counter when you are ready to eat some of the mints.