In a medium bowl, combine the tomatoes with 1/2 tsp. each salt and pepper.
Preheat a grill or grill pan to medium-high. Add the bread and grill, turning, until golden and charred in spots, about 5 minutes. Rub one side of each hot bread slice with the cut side of a garlic clove, using half a clove for each slice.
Drizzle 1 tbsp. EVOO evenly over the garlicky side of each bread slice and spoon the tomatoes on top. Sprinkle with the basil and drizzle with a few more drops of EVOO.