Preheat your oven to 300°F (150°C) and line a baking sheet with parchment paper or a silicone mat.
Cream together the softened butter and brown sugar using an electric mixer on medium speed until light and fluffy, then add the egg yolks and vanilla extract, mixing well.
Gradually sift in the all-purpose flour, red food coloring, and cocoa powder, blending on low speed until a soft dough forms.
Scoop heaping tablespoons of dough, roll into balls, and coat each ball in sugar before placing on the baking sheet.
Press into the center of each dough ball to create an indentation and bake for 10 minutes.
Prepare the cream cheese filling by blending cream cheese, egg yolk, sugar, salt, and additional vanilla until smooth.
Remove cookies from the oven, deepen the indentations, spoon in the cream cheese filling, and bake for an additional 12 minutes.
Allow cookies to cool completely on a wire rack before serving or storing.