Preheat your oven's broiler with a rack positioned about six inches below the heat.
Cut the loaf in half lengthwise, then slice it into two-inch pieces. Liberally brush each slice with olive oil and place them on a sheet pan. Broil for about three minutes, or until the bread turns a light golden brown.
Grate the ripe tomatoes using the large holes of a box grater, discarding the peels. Season the tomato pulp with a pinch of sea salt and a little lime juice, if you like.
Once the bread is out of the oven, rub the cut side of the garlic cloves over each warm slice. Spoon the grated tomatoes evenly over the toasted bread and serve immediately.