Make the cookies: Whisk the flour, cocoa powder, baking soda and salt in a medium bowl. Beat the butter, confectioners' sugar and vanilla in a stand mixer fitted with the paddle attachment on medium speed until smooth, about 1 minute. Reduce the mixer speed to low and beat in the flour mixture in 2 additions. Add the food coloring and beat until combined. Transfer the dough to a clean surface and knead a few times. Roll into a 10-inch-long, 1-inch-diameter log; wrap in plastic wrap and freeze until firm, about 2 hours.
Meanwhile, make the filling: Pulse the coconut, cream cheese, confectioners' sugar, salt and vanilla in a food processor until combined. Refrigerate until ready to use.
Preheat the oven to 350 degrees F. Line 2 baking sheets with parchment paper. Remove the dough from the freezer and unwrap. Slice the dough into 1/4-inch-thick rounds and arrange about 1 inch apart on the prepared baking sheets. Bake until the cookies are firm around the edges, 8 to 10 minutes. Let cool 2 minutes on the baking sheets, then transfer to a rack to cool completely.
Spread about 1 teaspoon of the filling on the flat side of half of the cookies, then sandwich with the remaining cookies.
Cook's Note: If the dough feels dry after you beat in the food coloring, beat in up to 2 more tablespoons softened butter until the dough stays together when pinched and is kneadable.