I've never had pickled eggs, but I love pickles. After I finish a jar, I save the pickle juice and then just cut up veggies, like carrots, string beans, or peppers, and stick 'em in the jar. They are actually just marinating, not like pickling from scratch - but after chilling for several hours or overnight, they will stay good for almost a week, and are great on top of salads.
Easy marinade:
1/2 cup olive or salad oil
1/2 cup lemon juice or vinegar
1 clove garlic, minced
2 tbsp sea salt
1/2 tsp dried basil*
1/2 tsp oregano*
Combine above ingredients, adjusting seasoning to your taste. Yields 1 cup of marinade. In a glass or ceramic container**, add 2 to 3 cups of cut-up veggies or beans (such as beets, broccoli florets, cabbage, cauliflower florets, carrots, celery, cucumber, mushroom, onions, bell peppers, sugar snap peas, sprouts, summer squash/zucchini, tomato, kidney beans, garbanzos/chick peas, or soybeans) and cover with the marinade.
Chill several hours or overnight, turning every so often with a wooden spoon. Use approx. 1/2 cup of veggies at a time, on salads, as a side dish, or mixed with other foods you like. Marinated veggies will last up to about 4 or 5 days. The marinade can be used again for about a week, but bits of veggies will start to spoil after that.
*Or substitute other herbs you prefer, such as dill and parsley, or tarragon.
**Glass or ceramic is preferred because metal containers may adversely react with the acidity of the marinade, and plastic will tend to hold in odors even after washing.
I got the above recipe from a 1978 book my mother gave me when I turned 18 and was getting ready to move out to be on my own, called The Return to Natural Foods Cookery by Kathleen LaCore. It's stained, beat-up, and falling apart, but I still use it for it's simple recipes and great tips. I reuse jarred pickle juice when I'm too lazy to make a marinade.
Re the pickled eggs, do they pickle the whole egg? is it boiled first? Methinks they would not be so gassy if a hole was poked in one end before boiling.