Start by chopping the tomatoes into even sized pieces and place in a medium sized bowl. With your hands (don't use a knife), rip the basil leaves into small pieces. Gently stir together the tomatoes and basil and then form a dome with the mixture.
Drizzle about 2 tablespoons olive oil over the dome and then sprinkle the salt on top. Do not stir in the olive oil or salt. Set aside, uncovered, at room temperature for 45 minutes to an hour to marinate (or as long as you have!)
Slice the bread and then brush 2-3 tablespoons of oil on the tops of the slices. Toast the bread slices on a charcoal grill (oiled side down) until golden-brown and lightly marked with grill lines OR: Set your oven rack about 6 inches from the heat source and preheat the oven's broiler to high. Place bread (oiled side up) on baking sheet and broil for 1-2 minutes (watch carefully) and then remove from the oven.
Slice a raw garlic clove in half. Gently rub the grilled slices of bread (both sides) with the cut end of a raw garlic clove.
Top each slice with the marinated tomatoes. Add a light drizzle of a bit more of the extra-virgin olive oil, if desired and any additional basil or salt on top. Enjoy immediately while the bread is still slightly warm.