Preheat the oven to 300°F (150°C). Line two large baking sheets with parchment paper.
In a large mixing bowl, beat the butter and 1/2 cup (100 g) granulated sugar together until light in color, about 5 minutes.
Add the egg yolk, 1 teaspoon vanilla extract, and red food coloring to the butter mixture, mixing until combined.
In a separate bowl, whisk together the flour and cocoa powder. Gradually mix the dry ingredients into the wet mixture until a soft dough forms.
Scoop the dough and shape it into 1-inch balls. Roll each ball in the coarse sugar to coat the outside.
Place the dough balls 2 inches apart on the prepared baking sheets. Press a deep indentation into the center of each ball using the back of a measuring spoon or your thumb.
Bake the cookies for 10 minutes. While they bake, prepare the filling by beating the cream cheese, 1/4 cup (50 g) granulated sugar, egg white, 1/2 teaspoon vanilla extract, and salt in a small bowl until smooth.
Remove the cookies from the oven. If the indentations have puffed up, gently press them down again. Spoon 1 teaspoon of the cream cheese filling into the center of each cookie.
Return the baking sheets to the oven and bake for another 10 to 12 minutes, or until the filling is set and reaches an internal temperature of 160°F (71°C) for food safety. Transfer the cookies to wire racks to cool completely.