Line two baking sheets with parchment paper and set aside.
In the bowl of a stand mixer, beat together the cream cheese and 2 cups of powdered sugar with the paddle attachment until evenly combined.
Add the peppermint extract, food coloring, and remaining 2 cups of powdered sugar to the bowl. Mix until combined and evenly colored. (You can add more green food coloring for a darker shade of green if desired.)
Use a 1-tablespoon cookie scoop to form balls of the mint mixture. Place the balls onto the prepared baking sheet.
Dip the back of a 1/2 teaspoon measuring spoon into some powdered sugar (to keep it from sticking) and press it into the mint balls to make a cavity (like a thumbprint cookie).
Chill the mints in the fridge for 1 hour.
Pour the chocolate chips into a heat-safe bowl. Heat the heavy cream in a small saucepan over medium heat until just beginning to boil. Pour the cream over the chocolate chips and let sit for 60 to 90 seconds. Whisk until the ganache comes together and is smooth.
Use a piping bag or a small spoon to fill the cavity in each cream cheese mint with ganache.
Chill the mints in the fridge for 2 hours so that the ganache can harden slightly.
Notes
Store the mints in an airtight container in the fridge. Let rest on the counter to soften the ganache a bit before enjoying them.
The yield for this recipe varies by how much ganache you put onto each mint. If you run low on ganache, you can reroll any remaining mints and use a fork to press them flat (like classic cream cheese mints). If you have extra ganache, you can spoon a little more onto each mint, if desired.