We use the following recipe with quail eggs (we raise quail for meat and eggs), but it works well with chicken eggs too. Given the ingredients, it may sound spicy, but they actually turn out pretty mild.
Siricha Pickled eggs
Fill quart jar with hard boiled eggs. In general proportions, add a brine made of (I eyeball it in the jar) …
1/3 siricha sauce
1/3 apple cider vinegar
1/3 water
To each jar, add 1/4 cup chopped onions, 1 clove smashed garlic, 1 t kosher salt, 1 t peppercorns, 1/2 t mustard seeds, and 1/2 t red pepper flakes. Shake well to mix ingredients and refrigerate. Chicken eggs take about a week. I don’t know how long they keep, they never seem to last more than a couple weeks.
Pickled egg pro tip. Soak your hard boiled eggs (in the shell) overnight in vinegar. The next morning they will be very easy to peel. Anyone who has tried to peel freshly laid eggs knows just what a pain that can be.