Preheat and Prepare Tins: Preheat oven to 350°F (175°C). Spray two regular-sized cupcake tins thoroughly with cooking spray to prevent sticking.
Mix Dry Ingredients: In a medium bowl, whisk together all-purpose flour, Dutch-processed cocoa powder, black cocoa powder, baking soda, and salt. Set aside.
Cream Butter and Sugars: In a large mixing bowl, beat unsalted butter, granulated sugar, and light brown sugar on medium-high speed until light, fluffy, and well combined, about 2 to 3 minutes.
Add Eggs and Vanilla: Reduce mixer speed to low. Add eggs one at a time, followed by vanilla extract. Beat until fully incorporated.
Combine Wet and Dry: Gradually add the flour mixture to the butter mixture and mix only until just combined. Do not overmix.
Scoop and Bake: Using a large cookie scoop or approximately 3 tablespoons, portion cookie dough evenly into prepared muffin tins. Bake for 10 to 13 minutes or until mostly set but still soft in the centers.
Create Wells: Immediately after removing from oven, press down firmly into the center of each cookie cup using a small jar or container to create a well for filling. Work quickly while cookies are hot.
Cool Cookies: Allow cookie cups to cool in pans for 10 minutes. Gently twist each cup slightly to loosen, continue cooling for 5 more minutes, then transfer to a wire rack to cool completely.
Whip Cream: Using a cold bowl and whisk, whip chilled heavy cream until stiff peaks form, about 3-4 minutes.
Mix Cheesecake Base: In a separate mixing bowl, beat cream cheese, granulated sugar, and peppermint extract together until smooth and creamy with no lumps.
Fold in Whipped Cream: Gently fold the whipped cream into the cream cheese mixture until fully combined and smooth, maintaining as much air as possible.
Prepare Piping Bag (Optional): Using a small food-safe paintbrush, paint two decorative red stripes on the inside of a piping bag fitted with a large round tip. Fill piping bag carefully with peppermint cheesecake filling.
Fill Cookie Cups: Pipe a generous swirl of cheesecake filling into each cooled cookie cup, filling right to the top.
Chill to Set: Refrigerate filled cookie cups for 1 to 2 hours or until the filling is completely set.
Garnish and Serve: Sprinkle chopped candy canes on top of chilled cookie cups just before serving. Keep refrigerated and consume within 2 to 3 days.