Boil the potatoes and haricots verts:
Put the potatoes and 2 tsp. salt in a large saucepan, add enough water to cover by 1 inch, and bring to a boil. Reduce to a simmer and cook until easily pierced with a wooden skewer, 15 to 20 minutes. Drain and let cool.
Fill the saucepan three-quarters full of fresh water and bring to a boil. Add the haricots verts and 1/2 tsp. salt to the water and cook until you can just bite through a bean with little resistance, 3 to 4 minutes. Drain, rinse with cool water to stop the cooking, and set aside.
Grill the potatoes and tuna:
Heat a gas grill to high or prepare a hot charcoal fire.
Combine 1 Tbs. of the mayonnaise and the honey in a small bowl. Season the tuna steaks with 1/2 tsp. salt and 1/4 tsp. pepper and coat both sides with the mayonnaise mixture. When the grates are very hot, grill the tuna until dark marks form on both sides, 1 to 2 minutes per side for medium rare. (If you prefer medium tuna, grill over medium-high heat for about 3 minutes per side.) Transfer to a cutting board and let rest for 5 minutes. Slice into 1/4-inch-thick strips.
Cut the potatoes in half and toss them in a mixing bowl with the remaining 2 Tbs. mayonnaise, the mustard, and 1/2 tsp. salt. Turn the grill to medium high or let the fire die down some. Grill the potatoes without disturbing except to flip, until brown grill marks form on both sides, 1 to 2 minutes per side.
Assemble the salads:
Set 6 large dinner plates on your counter. Put the red leaf lettuce, the arugula, and half of the basil in a large mixing bowl and toss with 2 to 3 Tbs. of the vinaigrette.
Divide the lettuce among the plates, piling it in neat, tall mounds at 12 o'clock. Combine the tomatoes and the remaining basil in the mixing bowl and toss with 2 to 3 Tbs. of the vinaigrette. Tuck the tomatoes in to the left of the lettuce and arrange the tuna to the right of the lettuce. Put the olives in the middle of each plate. Toss the green beans in the bowl with about 2 Tbs. of the vinaigrette. Arrange the grilled potatoes and the green beans at the bottom of each plate and tuck in the hard-cooked egg quarters wherever they look best. Drizzle a few teaspoons of the vinaigrette over the tuna and the potatoes on every plate. Serve right away.
nutrition information (per serving):
Photo: Scott Phillips