Place the 12 eggs in a saucepan and cover them with cold water by about 1 inch. Bring the water to a full boil, cover the pan, remove it from the heat, and let the eggs stand for about 10–12 minutes.

Transfer the cooked eggs to an ice bath and cool them completely. Peel the eggs carefully, rinsing away any small shell pieces if needed.

In a saucepan, combine the vinegar, water, sugar, salt, and pickling spice. Bring the mixture to a boil, stirring until the sugar and salt dissolve, then simmer or boil gently for about 5 minutes.

Place the peeled eggs and thinly sliced onion rings in a clean glass jar or other nonreactive container. Pour the hot pickling liquid over the eggs, making sure they are covered.

Cool the jar briefly, then cover it and refrigerate. Pickle the eggs for at least 8 hours, although 24–48 hours produces a stronger, more developed flavor.