Place peeled, hard-boiled eggs into a quart wide mouth mason jar (or use a half recipe for pint jars).
Place liquids (water/vinegar, etc) into a small saucepan and add sugar and salt. Gently heat until dissolved, then remove from heat.
Add spices and sliced veggies (onions/garlic/etc) directly into the jars.
Pour the hot brine over the eggs and spices, leaving as little headspace as possible (around 1/4 inch).
Seal jars with lids and allow them to cool slightly before storing them in the refrigerator.
Allow the eggs to pickle for at least 24 hours before eating, preferably around 1-2 weeks for better flavors.
Pickled eggs should last 3-4 months in the refrigerator.
Notes
Date the jars when you make the pickled eggs, but obviously, if there's any question as to whether or not they're good, when in doubt, throw it out.Do not can pickled eggs, there is no safe method for canning pickled eggs at home. They must be kept in the refrigerator at all times.