Place fingerling potatoes in a pot of salted water and bring to a boil; cook for 10 minutes, adding the green beans during the final 3 minutes of cooking.
Drain the potatoes and beans, then immediately plunge them into an ice bath to stop the cooking process and preserve the vibrant green color.
In a separate small saucepan, cover the egg with water, bring to a boil, then turn off the heat and let sit for 9 minutes before peeling and halving.
Whisk together the extra virgin olive oil, lemon juice, Dijon mustard, and half of the salt and pepper in a small bowl to create the vinaigrette.
Season the tuna steak with the remaining salt and pepper, then sear in a hot skillet with avocado oil for 1-2 minutes per side until golden on the outside but rare in the center.
Slice the tuna into thick strips and arrange on a bed of mixed greens alongside the potatoes, green beans, egg halves, olives, and capers.
Drizzle the prepared lemon-Dijon vinaigrette over the salad and serve immediately.