Put the onion in a small bowl. Add 1 tsp. salt and massage into the onion. Cover with 1/4 cup cold water. Let it rest for 5 minutes.
Drain and rinse the onion, then squeeze out the excess water using paper or kitchen towels.
In another small bowl, combine the onion, mayonnaise, eggs, pickle, parsley, 1/4 tsp. salt, and a few grinds of black pepper, and mix well. Cover and refrigerate until ready to use.