3 pounds Yukon Gold potatoes
1 tablespoon + 1 ½ teaspoons kosher salt, divided
1 ¼ cups mayonnaise
2 tablespoons finely chopped dill pickles
1 tablespoon dill pickle brine
1 tablespoon mustard
½ teaspoon freshly cracked black pepper
2 celery ribs
1 shallot
4 large hard-boiled eggs