Sprinkle tuna with pepper and ½ teaspoon salt. Heat 1 tablespoon oil in a large skillet over high. Add tuna, and sear until browned on both sides, about 2 minutes per side. Transfer to a cutting board; thinly slice.
Prepare haricots verts according to package directions. Remove from bag; transfer to an ice bath. Toss together beans, greens, and tomatoes in a bowl; place on plates. Top each with 2 egg halves.
Whisk together vinegar, shallots, mustard, and remaining ¼ teaspoon salt and 3 tablespoons oil. Drizzle over salads; top with tuna.