In bowl of stand mixer combine cream cheese and sweetened condensed milk, mixing on low speed until smooth. Add in eggs, one at a time, until combine. Add vanilla.
Divide batter in half. To one half, add in the 1/3 cup melted chocolate chips, stir until completely combined. Pour the chocolate batter into the prepared crust. To the other half, color with green food coloring to reach a pale, minty green color (remember, a little bit goes a long way!). Fold in the mint chips and peppermint extract. Pour mint chip batter evenly over the chocolate batter.
Bake for 45-55 minutes until center is set. Take care not to over bake. Cool cheesecake for 30 minutes on wire rack. Slightly loosen cheesecake from pan by running a knife around the edges, this will also help prevent cracking. Cover and refrigerate overnight before serving.
Keep leftovers tightly wrapped in the refrigerator.