Beat together cream cheese, pudding mix, and vanilla until light and fluffy. Roll into 2 tsp portions and freeze until completely frozen, about 30-40 minutes. 

Preheat the oven to 350°F. Line a large baking sheet with parchment paper.

Add butter and sugars to a large bowl. Use a handheld mixer to cream together butter and sugars until light and fluffy. Add the applesauce, vanilla, cream of tartar, baking soda, and salt. Beat until combined.

Add the flour. Beat on low until a soft dough forms. You may need to go in with a wooden spoon or rubber spatula to press the dough together. Fold in chopped Nilla wafers. 

Portion out dough with a 1.5-2 tbsp cookie dough scoop. Slightly flatten out then place a frozen cheesecake disc in the center. Close the cheesecake in with the cookie dough. Make sure the cheesecake is completely covered in cookie dough. Shape each cookie dough section into a slightly flattened disc, rather than a ball. 

Bake for 11-12 minutes. (Optional): To create perfectly round cookies, place a mug/glass or circular cookie cutter over the warm dough and do a little swirl to form a round cookie. Allow cooling on the baking sheet for 10 minutes before transferring to a wire cooling rack.

Once the cookies are completely cool, prepare the buttercream. Beat butter until smooth and fluffy, then slowly incorporate powdered sugar. Add milk and vanilla and beat until fluffy.

Top each cookie with buttercream, banana slice, and nilla wafer.