In large bowl, break up cookie dough. Stir or knead in cocoa and food color until well blended. Shape dough into flat disc; wrap tightly with plastic wrap. Refrigerate 30 minutes.
Heat oven to 350°F. Line 2 cookie sheets with cooking parchment paper.
Lightly dust work surface with additional baking cocoa. With rolling pin, roll out dough to 1/4-inch thickness. With 2-inch round cookie cutter, cut out 20 rounds. Combine leftover dough into ball; roll out and cut out 10 more rounds.
With small heart-shaped cutter, cut heart shapes from half (15) of the dough rounds. (These will be the tops of each cookie sandwich.)
Place all dough rounds 2 inches apart on cookie sheets.
Bake 10 to 12 minutes or until set. Cool on cookie sheets 1 minute; remove from cookie sheets to cooling racks. Cool completely, about 30 minutes.
In medium bowl, beat cream cheese, butter and vanilla with electric mixer on medium speed until creamy. On low speed, beat in powdered sugar one-third at a time until well blended.
Spread 1 heaping teaspoon frosting onto each cookie round without heart-shaped cutouts. Place 1 cookie round with heart-shaped cutouts on top.