Whisk the flour, cocoa powder, baking soda, and salt together until combined. Set aside.

In a large bowl using a handheld or stand mixer fitted with a paddle attachment, beat the butter, 1/2 cup granulated sugar, and the brown sugar together on high speed until completely smooth and creamy, about 2 minutes. Add the egg, milk, and vanilla extract and beat until combined, about 1 minute. Scrape down the sides and bottom of the bowl as needed.

On low speed, slowly mix the dry ingredients (flour mixture) into the wet ingredients until combined. Finally, beat in the food coloring. Add 1-2 teaspoons more for a brighter red, if desired. The cookie dough will be slightly sticky. Cover dough tightly with aluminum foil or plastic wrap and chill for at least 1 and 1/2 hours and up to 2-3 days.

In a large bowl using a handheld or stand mixer fitted with a paddle attachment, beat the cream cheese, confectioners’ sugar, flour, and vanilla extract together on medium-high speed until completely smooth and creamy, about 3 minutes. Drop teaspoonfuls onto a lined baking sheet that will fit in your freezer. Freeze for at least 1 and 1/2 hours and up to 2-3 days.

Remove cream cheese spoonfuls from the freezer. Roll each into a ball as best you can. It will be a little sticky. Place in the refrigerator until ready to use in step 7. You want them as cold as possible!

Preheat oven to 350°F (177°C). Line two large baking sheets with parchment paper or silicone baking mats. (Always recommended for cookies.) Set aside.

Remove cookie dough from the refrigerator. If the cookie dough chilled longer than 3-4 hours, let it sit at room temperature for about 20 minutes. This makes the cookie dough easier to scoop and roll. Roll cookie dough, 1 Tablespoon each, into balls. Using your thumb, make an indent into one cookie dough ball. Remove cream cheese balls from the refrigerator. Place one inside the indentation. Cover the cream cheese ball with another cookie dough ball and mold the two dough balls around the cream cheese, making sure it is completely covered and snug inside. Repeat with remaining cookie dough and cream cheese.

Roll each stuffed cookie dough ball in remaining granulated sugar and arrange 3 inches apart on the baking sheets. Bake for 12-13 minutes or until edges appear set. Centers will look soft.

Remove from the oven and allow cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.

Cookies will stay fresh covered at room temperature for 3 days or in the refrigerator for 1 week.