In a large bowl, beat the butter with an electric mixer until soft. Beat in the cream cheese until smooth and incorporated.
Add in the peppermint extract. Mix in the powdered sugar starting with the mixer on low speed and incorporating about 1 cup at a time.
Divide the mixture into different bowls, add in a few drops of food coloring into each and mix until the color is even.
Dust your hands with powdered sugar and form the dough into small balls and place on the lined cookie sheets. Dip a fork into powdered sugar, then gently press into the top of each ball.
Let the mints sit at room temperature for about 2 hours for a crust to form, then place in the fridge to firm up even more.
Notes
Store mints in an airtight container in the fridge. Mints can be frozen for up to 2 months.