In a large mixing bowl, combine the flour, sugar, baking powder, salt, and cream of tartar. Cut in the shortening with a pastry blender. Add the grated cheese, green bell pepper, and pimento; mix with a fork. Stir in milk and mix well.
Turn the dough out onto a floured surface and knead 5 times. Roll out to a rectangular shape and cut into squares using a knife or pizza cutter. Place onto an ungreased baking sheet.