For the salad: In a small bowl, toss potatoes, green beans, and grape tomatoes with the 2 teaspoons vegetable oil, salt and pepper. Arrange the vegetables in a single layer in air fryer basket. Set fryer to 400°F for 10 minutes, shaking halfway through cook time.
After 10 minutes of cook time, brush tuna on both sides with a 1 tablespoon vegetable oil and season to taste with salt and coarsely ground pepper. Press the salt and pepper into the tuna so they will stay put. Add tuna to basket on top of the vegetables. Cook for 5 minutes for tuna that is cooked medium-well.
At end of cook time, remove tuna and let it rest for 5 minutes. Slice tuna thinly across the grain.
Meanwhile, for the vinaigrette: Combine vinegar, salt, mustard, olive oil, black pepper, and Herbes de Provence to taste in a small jar with a lid. Shake to combine.
Place 3 lettuce leaves on each of two dinner plates. Arrange tuna, green beans, tomatoes, and potatoes in small piles on lettuce. Place 2 egg halves on each plate. Scatter olives over. Drizzle all with the vinaigrette. Serve immediately.