In a mixing bowl, beat shortening, butter, sugar, and eggs. On low speed, beat in the flour, salt, baking powder, and vanilla until incorporated. Increase speed to medium and beat until well blended.
Divide the dough into three separate bowls. Mix red food coloring into one bowl--you'll need quite a bit to get a deep, rich color. Do the same to another bowl using green. Keep the third bowl plain.
Roll out each color on separate pieces of waxed paper to about ⅛-inch thickness, making them all about the same size. Carefully flip one on top of the other, lining up the edges of the dough as much as possible and removing the waxed paper after flipping. Once stacked, use a pizza cutter to trim the edges straight.
Starting at one long side, roll the layers tightly together, lifting up the waxed paper underneath to help roll. Wrap the waxed paper around the roll and chill overnight.
Preheat your oven to 375 degrees. Use a sharp knife to cut dough into ⅝-inch thick slices. Roll the edges in decorating sprinkles and set slices on a parchment paper-lined cookie sheet. Bake about 10 minutes, until just barely done.