Trim any skin or dark spots from the tuna steaks, then lightly oil both sides and generously season with the pepper.
Put the vinegar in a medium bowl and whisk in the remaining olive oil.
Stir in the garlic, olives, tomatoes, mozzarella, and basil.
Set aside.
Set up your grill for direct grilling and preheat to medium-high.
Arrange the tuna steaks on the grill grate and grill, turning once, until the steaks are marked on the outside and the desired degree of doneness is reached, such as 3 to 4 minutes per side for medium-rare.
Indoors, you can use a grill pan or contact grill, or even a cast iron skillet to sear the steaks.
Transfer the steaks to plates and divide the salad between them.
Garnish with fresh sprigs of basil.
Serve with lemon wedges for squeezing.
Yields 4 generous servings.