Pan con Tomate -- Bread with Tomato

Makes about 1/2 cup of tomato topping, enough for about 8 pieces

2 medium-large tomatoes firm-ripe ones at peak flavor
1 large clove garlic
2 - 4 tablespoons olive oil extra virgin
1 teaspoon sea salt
1 loaf baguette or other firm, crusty bread (Reserve the remainder for another use.

Cut the tomatoes in half crosswise. Using the large holes of a box grater, carefully grate the fleshy side into a bowl. You should only have the thin skin remaining. This will yield about one cup of grated tomato.
Transfer the grated tomato through a fine mesh strainer into another bowl, reserving the juice to add back as needed to create a tomato spread the viscosity of a jam or jelly. (Remember, tomatoes are technically a fruit!)
Cut the baguette into 3-inch lengths, then slice each piece in half crosswise. Place the sliced pieces cut side up and broil until lightly toasted, about 4 minutes. (A toaster oven is ideal here!) Reserve any remaining bread for another use.
Rub the clove of garlic across the toasted bread. Start on the crispier edges to break through the garlic. Go lightly as this method imparts a lot of garlic-iness, and you want to have the tomatoes shine here.
Spread the jammy, fresh tomato onto each piece. Drizzle each piece with extra-virgin olive oil and sprinkle with sea salt.
Serve immediately. Some absorption of the tomatoes into the bread is desired, but you want to avoid a soggy bread.