You can use either hard-boiled eggs or empty intact eggshells.
Once the egg is completely dry, place it into the second batch of dye. Roll the egg once around the dye. The food coloring only dissolves in the water and not in the oil. Thus the surface of the egg that touches the oil will not collect any dye while those that touch the water will absorb color, creating the marbleized effect. If you want more of the egg's original color to show through, add more vegetable oil to the dye.