Preheat the oven to 325°F. Line a standard muffin tin (use one or more tins as needed) with cupcake liners so you have one liner per mini cheesecake.
Place the white chocolate chips (1 cup) in a microwave-safe bowl. Microwave in 30-second increments, stirring between each interval, until smooth and fully melted. Set the melted white chocolate aside to cool to room temperature while you make the crust.
In a medium bowl, combine the mint Oreo cookie crumbles (1½ cups), 3/8 cup granulated sugar, and the 3 tablespoons melted butter. Stir until the crumbs are evenly moistened.
Divide the crumb mixture among the lined muffin cavities. Use about 1 tablespoon of crumbs per cavity (adjust slightly if using fewer/more cavities). Press the crumbs firmly and evenly into the bottom of each liner with the bottom of a cup or a small tamper to form compact crusts.
In a large mixing bowl, beat the softened cream cheese (16 ounces) until smooth and fluffy, scraping the sides of the bowl as needed.
Add 2/3 cup granulated sugar, 1 teaspoon peppermint extract, and 1 teaspoon vanilla extract to the cream cheese. Beat until fully combined and smooth.
Beat the cooled melted white chocolate into the cream cheese mixture, then stir in 1/2 cup sour cream until combined. Taste and adjust the mint flavor if desired (using only the peppermint extract provided).
Add the eggs (2) one at a time, gently mixing by hand or on low speed after each egg until just combined. Do not overmix.
Add 1 to 2 drops gel-based green food coloring, mixing by hand until the color is even; add up to the 2 drops provided until you reach the desired shade.
Fold in the finely chopped mint Oreo cookies (6 cookies) until evenly distributed in the batter.
Spoon or pipe the cheesecake filling over the packed crusts, filling each liner almost to the top and smoothing the tops as needed.
Bake at 325°F for about 20 minutes, or until the mini cheesecakes are set and the tops are dry to the touch. Remove from the oven and let cool to room temperature (about 30 minutes).
Once cooled, transfer the cheesecakes to the refrigerator and chill for 1 to 2 hours to firm up.
While the cheesecakes chill (or right before serving), make the chocolate whipped cream: in a chilled bowl, whip 2 cups heavy whipping cream with 4 tablespoons cocoa powder and 6 tablespoons powdered sugar until stiff peaks form.
Pipe or dollop the chocolate whipped cream onto each chilled mini cheesecake and top each one with an Andes mint (use the 18 Andes mints provided, one per cheesecake). Serve chilled.