Dice tomatoes into ½-inch pieces. Place in a fine mesh strainer, sprinkle with ¼ teaspoon salt, and let drain for 10 minutes.
Transfer drained tomatoes to a bowl. Add torn basil, minced garlic, olive oil, balsamic vinegar, remaining salt, and pepper. Toss gently. Taste and adjust seasoning.
Rest the tomato topping at room temperature for 15 minutes.
Brush bread slices with olive oil. Toast in a 400°F oven for 6 to 8 minutes turning once, or in a hot grill pan for 2 minutes per side, until golden and crisp all the way through.
Immediately rub the cut side of the halved garlic clove firmly across the surface of each hot toast slice.
Spoon the tomato mixture generously over each garlic toast, draining any excess liquid first. Drizzle with olive oil and balsamic glaze if using. Scatter extra basil, crack pepper over the top, and finish with flaky sea salt. Serve immediately.