Bring a large metal sauce pan with six cups water to a boil with one tablespoon sea salt. Wash and slice three cups fingerling potatoes. Add potatoes to boiling water, reduce heat to medium high and cook for ten minutes. Remove pan from burner and allow to cool for five minutes. Run cooked fingerling potatoes under cool water, then strain water from pan and set aside. In a small glass jar, mix together three tablespoons scallion infused olive oil, two tablespoons cherry honey mustard, one tablespoon wild leek vinegar and season to taste with salt and pepper. Remove one cup of purslane leaves from stems, rinse under cool water, pat dry and add to a large glass mixing bowl. Chiffonade two tablespoons lemon basil leaves and add to the mixing bowl. Slice one half cup shallots, separate into rings and add to the mixing bowl. Stir in cooled potatoes. Slice three steamed eggs in half and remove yolks. Slice the egg whites and and add to the mixing bowl. Gently stir in dressing before serving salad.