In a large mixing bowl, combine the cream cheese, softened butter, vanilla extract, and peppermint extract.
Gradually add the powdered sugar to the bowl, mixing continuously to avoid a sugar storm. Keep adding until the sugar is fully incorporated.
Test the mixture by forming a small ball with your hands. It should not be sticky. If it's sticky, add more powdered sugar, starting with ¼ cup. Mix well and test again, adding more sugar if necessary.
Divide the mixture into separate bowls, one for each color you plan to use. Add a small amount of gel food coloring to each bowl and mix well. Add more coloring gradually until you achieve the desired shade.
Line a cookie sheet with parchment paper. Using a teaspoon or a small cookie scoop, scoop out portions of the mixture. Roll each portion between your palms to form a ball, then place it on the prepared cookie sheet.
Press down each mint ball with a fork to flatten slightly and create a pattern. Leave the mints to dry at room temperature for at least 2 hours.