Boil eggs until hard-cooked, about 9 minutes. Cool in ice water, peel, and chop.
Prep tomatoes, green onions, and parsley. Seed tomatoes and pat dry to limit moisture.
Whisk mayonnaise, lemon juice, hot sauce, pepper, and salt in a large mixing bowl.
Fold in chopped eggs, tomatoes, green onions, and parsley until coated.
Gently stir in crushed crackers just before serving. Mix only until combined.
Taste and adjust seasoning. Serve right away for the best crunch.