Peel and roughly chop the eggs. Thinly slice (chiffonade) 12 leaves of basil. Finely mince the 1/2 red onion.
In a bowl, combine the eggs, basil, and red onion with 1/2 cup Greek yogurt, 2 tablespoons Dijon mustard, 1/2 teaspoon kosher salt, and fresh ground pepper. Taste and add more seasonings as desired. Keeps for two days refrigerated (add additional fresh basil when serving for a fresher taste).