Prepare the filling by whisking the vegan cream cheese and powdered sugar until smooth. Place 12 small dollops onto a tray lined with parchment paper and freeze for at least 30 minutes.
Preheat oven to 350°F (175°C) and line two large baking sheets with parchment paper.
In a small bowl, combine flaxseed meal and water; let sit for 5 minutes to thicken into a flax egg.
In a large bowl, cream together the vegan butter, brown sugar, and granulated sugar until light and fluffy.
Mix in the flax egg, vanilla extract, and red food coloring until the color is uniform.
Sift in the flour, cocoa powder, baking soda, and salt. Mix until a soft dough forms.
Divide the dough into 12 equal portions (approximately 2 tablespoons each).
Flatten a portion of dough in your palm, place a frozen cream cheese dollop in the center, and fold the dough around it, pinching to seal completely.
Place the balls on the prepared baking sheets, spaced 2 inches apart.
Bake for 10 to 12 minutes until the edges are set but the centers remain soft.
Allow cookies to cool on the baking sheet for at least 10 minutes before transferring to a wire rack to firm up.