Cut the loaf into eight 1/2" pieces. Turn on the broiler. You can alternatively grill the bread. See below for instructions.
While it's heating up, make the tomato mixture. In a medium bowl, mix together the basil, garlic, 1/4 teaspoon salt, pepper, 1 teaspoon olive oil, and balsamic vinegar. Once combined, add the tomatoes and halved mozzarella balls. Set aside, while prepring the bread, but not for too long - it gets watery. It's good to let it sit for 10-15 minutes for the flavors to meld but I don't recommend letting it sit much longer.
Pour 2 tablespoon of olive oil in a little bowl and brush the bread with olive oil (if grilling, oil both sides). Use more oil, if needed. Sprinkle the tops of the bread slices with a little salt. Place the bread under the broiler. You'll need 2–4 minutes, or until the edges are golden brown and the tops feel crisp to the touch.
If grilling, grill the bread slices over indirect heat, on both sides, until golden brown. Remove from the grill.
Remove from the oven / grill and top with the tomato mixture. Serve immediately.