Preheat oven to 375°F. Place racks in the top third and bottom third of the oven.
Place the chocolate and butter in a large microwave-safe bowl. Heat on HIGH in 30-second intervals for a total of 90 seconds, stirring with a wooden spoon after each interval.
Stir in the sugar, eggs, and red food coloring until fully combined and smooth.
In a separate bowl, whisk together the flour, cocoa, baking powder, baking soda, and salt.
Gradually mix the flour mixture into the melted chocolate mixture. The batter will very thick, and requires a little elbow grease as you mix. This process can also be done in a stand-mixer, just don't over mix the batter.
Place ½-cup of the powdered sugar in a medium-sized bowl. Use a trigger-handle ice cream scoop, or a couple of tablespoons to form a small ball of batter. Drop into the powdered sugar and turn to fully coat. Place on a baking sheet lined with parchment paper. Use the heel of your hand to gently flatten the ball just a bit. Dough balls should be spaced 1 inch apart from each other. You'll have enough dough to make between 24 to 30 cookies, depending on the size of your dough balls.
Bake the cookies for 11 to 12 minutes, until slightly fluffed. Remove from the oven and use a spatula to transfer the cookies to a baking rack. Cool for 20 to 30 minutes until completely cooled.
Meanwhile, place the softened cream cheese in a medium-sized bowl. Add 2 cups of the powdered sugar with the vanilla extract. Use a hand mixer to beat until smooth.
Spread about 1 tablespoon of the cream cheese filling over the flat side of half of the cookies. Press the remaining half of the cookies, flat side down, into the filling of the frosted cookies. Serve at once or store in an air-tight container with a lid.