In a medium-sized bowl, combine the cream cheese, sugar, peppermint extract, and food coloring (if using). Use an electric mixer to blend the ingredients until the mixture is smooth and well combined.

Portion out 10 even spoonfuls of the mixture onto parchment paper. Transfer to the freezer to set while preparing the cookie dough.

In a separate, small bowl, sift together the all-purpose flour, cocoa powder, baking soda, and salt. Set aside.

In a large mixing bowl or the bowl of a stand mixer fitted with the paddle attachment, cream together the butter, granulated sugar, and brown sugar until the mixture is light and creamy.

Beat in the egg and vanilla extract until well incorporated.

Gradually fold in the dry ingredients until the dough is homogeneous.

Divide the dough into 10 equal portions and place them on a plate lined with parchment paper. Cover the portions with plastic wrap and refrigerate for a minimum of two hours or up to 24 hours.

Preheat the oven to 350°F/180°C. Line a baking sheet with parchment paper.

Remove the cookie dough and cream cheese filling from the refrigerator. Flatten a portion of the cookie dough in your hand, place a set cream cheese dollop in the center, and encase the filling with the dough. Roll the filled dough between your palms to form a smooth ball. Repeat with the remaining dough and filling.

Place the filled cookie dough balls on the prepared baking sheet, ensuring they are spaced at least 2 inches apart.

Bake in the preheated oven for 11-12 minutes, or until the cookies have puffed up.

Remove from the oven and allow the cookies to cool on the baking sheet for 10 minutes. Afterward, transfer them to a wire rack to cool completely.