Preheat oven to 350°F and spray two regular-sized cupcake tins with cooking spray.
Whisk together all-purpose flour, Dutch-processed cocoa powder, black cocoa powder, baking soda, and salt.
Beat unsalted butter, granulated sugar, and brown sugar on medium-high speed until light and fluffy, about 2 to 3 minutes.
Reduce mixer speed, add eggs one at a time, then add vanilla extract and beat until combined.
Fold in the flour mixture just until combined.
Using a 3-tablespoon cookie scoop, portion dough into muffin tins.
Bake for 10 to 13 minutes until mostly set but still soft in the center.
Remove from oven and immediately press the center of each cookie down firmly with a small jar or container to create a well.
Cool the cookie cups in the pans for 10 minutes, loosen slightly by twisting, then cool for 5 more minutes before transferring to a wire rack to cool completely.
Whip chilled heavy cream until stiff peaks form using a cold whisk and bowl.
In a separate bowl, beat cream cheese, granulated sugar, and peppermint extract until smooth.
Fold whipped cream gently into the cream cheese mixture until combined.
Use a small food-safe paintbrush to paint two stripes of red color gel inside a piping bag fitted with a large round tip.
Fill the piping bag with peppermint cheesecake filling and pipe swirls into cooled cookie cups.
Refrigerate the filled cookie cups for 1 to 2 hours until set.
Sprinkle with chopped candy canes before serving.
Serve chilled and consume within 2 to 3 days or freeze without candy canes for up to 4 weeks.