Preheat the broiler on high for 10 minutes. Arrange the toasts on a baking sheet. Toast until edges are browned, about 2 minutes per side.
Meanwhile, slice the bottoms off of 2 of the tomatoes and grate into a bowl with the large holes on a box grater (the pulp will grate up while the skin will stay intact). If mixture is very watery, go ahead and grate a 3rd tomato. Add sherry vinegar and chili paste, if using, and sea salt to taste (start with ½ teaspoon flaky sea salt).
Rub toasts on both sides with the garlic clove. Drizzle toasts with olive oil, and sprinkle with sea salt and pepper.
When ready to serve, spoon the tomato pulp onto the toasts. Finish with olive oil, sea salt, and pepper, and, if desired, slice into triangles. If you’d like, serve with anchovies and olives.