Add the eggs to the bottom of a large pot and then add all the other ingredients. Bring to a boil and then reduce the heat to a simmer for 15 minutes. Using a slotted spoon or a pair of tongs, remove the eggs to a large bowl. Pour the liquid from the pot over the eggs (discarding the cabbage leaves) and then refrigerate overnight. I left mine in the refrigerator for 10-12 hours.
Do not panic if your eggs still look white when you transfer them from the pot to the bowl. Mine were still white and I had no idea if this was going to work at all, but it did in the end. The purple liquid actually turns blue overnight and the eggs do as well. When they are as dark as you like, remove them from the dye and blot dry with a cloth or paper towel. Store in the refrigerator until ready to eat. Enjoy!