Preheat an outdoor grill or a grill pan to medium-high. Drizzle EVOO on both sides of the tuna steaks; season with salt and pepper.
In a medium pot, cover the potatoes with cold water and bring to a boil. Salt the water, lower the heat and simmer for 10 minutes. Add the beans; cook for 4 minutes.
While the potatoes cook, using a food processor, puree the basil, pine nuts, garlic, lemon peel, 1 1/2 teaspoons salt and 1/2 teaspoon pepper. With the machine on, pour in the 1/3 cup EVOO in a steady stream. Transfer the pesto to a large bowl and stir in the cheese.
Grill the tuna steaks for 2 minutes on each side for medium-rare.
Drain the potatoes and beans, add to the pesto and toss to coat; season to taste with salt and pepper. Serve alongside the tuna steaks.