Place a rack in the center of the oven, and preheat the oven to 350 degrees.
For the cookie, place the cake mix and cocoa in a large mixing bowl and stir to combine. Add the egg, melted butter, and red food coloring. Beat on low speed with an electric mixer until the dough is thick, 1 to 1½ minutes.
Form the dough into 1½-inch balls and place these on ungreased cookie sheets about 1½ inches apart. Gently press down onto the balls to slightly flatten them. Place the pans in the oven, and bake until the cookies are slightly firm, 9 to 10 minutes. Using a metal spatula, transfer the cookies to a cooling rack. Cool 10 minutes before filling.
For the filling, place the confectioners’ sugar, shortening, soft butter, egg white, and vanilla in a large bowl and beat on low speed with an electric mixer until the ingredients are just incorporated, 15 seconds. Increase the mixer speed to medium-high and blend 1 minute, or until smooth.
Place 1 heaping tablespoon of filling onto the flat side of half of the cookie portion of the Whoopie Pies. Spread the filling almost to the edge. Place the remaining cookies on top of the filling, creating a sandwich and pressing down gently. Serve at once or store.