Whisk together the Egg (1), Lemon Juice (1 tablespoon), Dijon Mustard (1 tablespoon), Salt and Ground Black Pepper (1 dash). Start beating vigorously while slowly drizzling in the Olive Oil (1 cup). Beat until thick and smooth.
Preheat the broiler to high. Season both sides of each Boneless, Skinless Chicken Breast (2) with Kosher Salt (1 dash) and Ground Black Pepper (1 dash).
Mix mayo, Yellow Mustard (1 tablespoon) and Tarragon (3 tablespoon) together.
Grease a broiler pan with olive oil. Place breasts on the pan and spoon half (or a little less than half) of the mayo-mustard mixture over the breasts.
Broil 3 minutes. Remove pan. Flip breasts. Spread remaining mayo-mustard mixture over the breasts. Return to the broiler and cook for about 5 to 6 minutes longer, depending on the thickness of the breasts.