Combine all ingredients in a small bowl and stir until fully incorporated; set aside.
For the sandwich:
Season the tuna generously with salt and pepper on both sides. Heat 1 teaspoon of the oil in a medium frying pan over high heat until smoking. Add the tuna and sear until lightly browned on one side, about 1 to 2 minutes. Turn and sear on the other side, about 1 minute more for rare. Remove to a cutting board and let rest while preparing the remaining ingredients.
Placee the greens, olives, onion, remaining 1 teaspoon oil, and vinegar in a medium, nonreactive bowl. Season with salt and pepper and toss to combine. Slice the cooked tuna on the bias into 1/2-inch-thick pieces.
Divide the mayonnaise between the slices of bread and spread evenly. Top one slice of toast with half of the salad mixture, then half of the sliced tuna, then half of the egg slices. Repeat with the second piece of toast and serve open-faced.