First, boil and peel the eggs. For this batch, I hard-boiled the Eggs. However, you could also have a slightly soft-boiled yolk too - like these soy-marinated Ramen Eggs.
I know that there are so many different preferred ways of cooking eggs, so I suggest you use your favorite method. I usually cook the eggs for around 6 minutes for a softer center and 10 for hard-boiled. Then, either plunge the eggs into ice water to stop them cooking or run under cold water from the tap.
To prepare the pickling liquid, simply mix all of the ingredients in a large jar. I usually keep a few slices of the pickled beetroot in the brine too.
Add the eggs to the jar and place a layer of parchment paper in the jar to make sure than the eggs are fully submerged in the brine.
Cover and store in the fridge for at-least 12 hours. After 12 hours, the eggs will already be ready to eat and 'slightly pickled' - though 3 days within the brine is when they're at their best.The longer you keep the eggs in the pickling liquid, the deeper the color will penetrate the eggs. Sometimes even managing to reach the yolk. The color can vary from pale pink pickled eggs to deep pickled red beet eggs that are red/purple in tone.
You can use the leftover pickled beet juice (once the eggs are eaten) to pickle a further round of eggs too. Just leave them in the solution for a day or two and they'll become a lovely pink.
The total time does not include the time for coloring (marinating) the eggs. It's best to leave them in the fridge for at least 12 hours before you enjoy them.
Feel free to experiment with different pickling spices such as adding cardamom pods, star anise, cumin, chili, kimchi, mustard seeds, etc.
For a spicy version, feel free to add a jalapeno or two to the pickling liquid, seeds removed.
You can use canned beets or cook them yourself and then use the beet juice from the cooked beets.
TOP HACK: The simplest of all 'hacks' is to just buy some jars/cans of pickled beets then use the brine from those for your eggs and allow them to sit for a few days with no additional vinegar or flavorings. Easy peasy!