Place the tomatoes, bread, bell pepper, onion, and garlic in the bowl of a food processor fitted with the steel blade or in the glass jar of a blender and puree until you can only see tiny bits of the tomato skins. Pour the puree into a large bowl and whisk in the tomato puree, sherry vinegar, 2 teaspoons salt, and 1 teaspoon pepper. Slowly whisk in the olive oil, cover, and refrigerate for just 2 hours for the flavors to blend. (If you refrigerate the soup for more than 2 hours, prepare the soup without the olive oil, refrigerate, and whisk in the olive oil before serving. The olive oil congeals in the soup if you refrigerate them together for more than 2 hours.)
Serve cold in shallow bowls and top with the warm toasted croutons, halved cherry tomatoes, julienned basil leaves, flaked sea salt, and a drizzle of olive oil.
To toast croutons, pour 2 tablespoons of the olive oil in a small (8-inch) saute pan and heat over medium-high heat until a drop of water splashed in the pan sizzles. Add the bread cubes and saute, tossing occasionally, for 4 to 5 minutes, until the bread is evenly browned. Sprinkle generously with salt and pepper.