Gather your ingredients and tools.
Begin making the hard-boiled eggs following the 5-5-5 method (recipe found here). While the eggs are cooking, prepare the beets and carrots. Cut the beets in half and then into thick slices. Be sure to pour all of the beet juices from the package into your pickling container. Set beets aside.Note: I prefer to use a plastic cutting board to keep it from getting stained by the beet juice. Depending on your carrots, you may want to peel them, but if the are young you can probably just brush them under running water. Cut into 6 inch pieces and quarter them lengthwise to make thin sticks. Set aside with beets.
Into the pickling container along with all of the juice from the beets, add the apple cider vinegar, sugar, salt, and pepper. Stir well with large spoon or silicone spatula.
By now your eggs should be cooked, and cooled so you should be able to peel them easily. Put a layer of sliced beets in the pickling liquid. Peel one egg and drop it into the liquid, setting it on top of the beets.
Continue to peel the eggs and putting them in the pickling liquid. When you have a layer of eggs, add another layer of beets. A layer of carrots, then another layer of eggs, etc. You want to have all of the eggs completely submerged under the beets. Don't over-pack the container.Note: I didn't add the carrots in my photos until after the eggs were pickled, so you don't see them in the pics. Whatever veggies you are pickling can be added now. Just make sure the eggs aren't sticking out of the juices. Cover the container and put it into the refrigerator for at least 2 days. Every day, or a couple of times a day, you should take the container out and give it a shake (if water-tight!) or a stir to make sure all of the sugar is completely dissolved, and the beet juices are evenly distributed.
After 2 days, take an egg out and slice it to see how well the eggs have been infused with the pink beet juices. You should also test the beets and other veggies for the amount of pickling on them. The longer they stay in the juices, the more tart they will be.
If the eggs, beets and carrots are at the desired pickling level, drain off the juices. The pickled eggs and veggies can be stored in the airtight container for a few days.
I like to use an egg slicer to get perfect slices. They look so beautiful on the plate!
Enjoy experimenting with different veggies!