Preheat your indoor or outdoor grill to medium-high. Brush the tuna with 2 Tbsp. of the olive oil; season with salt and pepper. Grill 3 to 4 minutes, turning occasionally, or until nicely coloured on the outside, but still rare in the middle. Cool tuna to room temperature, and then cut into small cubes and place in a bowl. Toss in the tomatoes, basil, vinegar and remaining 2 Tbsp. olive oil.
Set an oven rack six inches below your oven’s broiler. Preheat the broiler to high. Rub the bread slices with the cut garlic and set on the baking sheet. Broil the bread until lightly toasted. Let the bread cool a few minutes, and then set on a platter. Top the bread with the tuna mixture. Divide and top the tuna mixture with nuggets of the cheese. If desired, before serving, drizzle each bruschetta with a little olive oil.
Note: Albacore tuna loins are oblong, boneless pieces of tuna. They are sold in our seafood department. The baguette used in this recipe was about 3 inches wide.