In a sauce pan, add eggs and enough water to cover by 1 inch. Bring to a boil, turn down heat and simmer for 15 minutes. Drain and put into a bowl covered with water and add ice cubes. Let sit in water till needed.
Put potatoes and 1/2 t. Kosher salt in a saucepan, add water to cover by 1 inch. Bring to a boil, reduce to a simmer and cook for 15-20 minutes. Drain and let cool. Set aside.
Fill saucepan 3/4 full of water and bring to a boil. Add the beans and 1/2 t. salt and cook for 3-4 minutes. Drain and rinse with cool water. Set aside.
Make vinaigrette. In a food processor, add garlic, and basil and process till finely chopped. Add the vinegar, lemon juice, red pepper flakes and process till smooth. Slowly add the oil. Season with salt and pepper.
This can all be done ahead of time.
Heat grill or grill pan. In a small bowl, combine 1 T. mayonnaise and honey. Season tuna with salt and pepper and coat both sides with the mayonnaise mixture. When grill is hot, grill the tuna for 3-5 minute per side for medium. Transfer to a plate and let rest for 5 minutes.
In a medium bowl, mix 2 T mayonnaise, Dijon and 1/2 t. salt. Cut the cooled potatoes in half and toss with mixture. Grill on medium high heat for 1-2 min per side without disturbing to make grill marks.
Divide Romaine, spinach, basil, between serving plates. Use 1-2 T. of basil vinaigrette for each plate and mix lightly together. Top with beans, tomatoes, olives, and eggs in bunches. Arrange grilled potatoes, and tuna on the plates and drizzle with as much of the basil vinaigrette as you like.