Beat butter and shortening in a large mixing bowl with an electric mixer on medium to high speed for 30 seconds. Add granulated sugar, baking powder, and salt; beat until combined, scraping sides of bowl occasionally. Beat in egg, orange juice or milk, and vanilla until combined. Beat in as much flour as you can with the mixer. Stir in remaining flour with a wooden spoon. Turn dough out onto waxed paper and knead in enough red food coloring for desired color. Divide dough in half. Cover and chill dough for 3 hours or until easy to handle.
Stir together egg white and water. Roll each half of dough on a floured surface until 1/4 inch thick. Cut with a floured 3-inch round cookie cutter. Cut cookies in half. Using a small brush, brush egg white mixture on rounded edge and in a 1/4-inch-wide strip on the front of each cookie. Dip brushed edge in coarse green sugar. Place on an ungreased cookie sheet. Press a few chocolate pieces into each cookie for seeds.
Bake in a 375 degree F oven for 5 to 7 minutes or until bottoms begin to brown; do not allow to brown on top. Transfer to wire racks and cool. Makes 48 cookies.