Preheat oven to 400°F. Remove crust from bread, and discard or reserve for another use. Cut loaf into 1-inch-thick slices; cut slices into 1-inch-wide strips. Tear strips into 1-inch pieces, and toss with oil until evenly coated. Spread in an even layer on 2 rimmed baking sheets. Bake croutons on separate oven racks in preheated oven 8 minutes. Continue to bake until golden brown and crisp, 18 to 22 minutes, flipping croutons and rotating pans (top to bottom) often to ensure even browning. Remove croutons from baking sheets as they finish browning. Sprinkle croutons with kosher salt, and let cool in a single layer.

Stir together shallots, red wine vinegar, and balsamic vinegar in a medium bowl; let stand 15 minutes. Cut tomatoes in half, and grate cut sides on large holes of a box grater until only skin remains. Discard skins. Set aside 1 cup tomato pulp. (Reserve remaining tomato pulp for another use.) Stir tomato pulp, oil, basil leaves, garlic, and kosher salt into vinegar mixture; let stand at least 10 minutes or up to 30 minutes. Remove and discard garlic. (Taste vinaigrette with a crouton or tomato slice, and adjust salt and acid as needed.) Set aside 1 1/4 cups vinaigrette; reserve remaining vinaigrette for another use.

Toss together onion and vinegar in a small bowl; let stand 20 minutes. Set aside. Place half of croutons in a large salad bowl, and toss with 1/2 cup reserved vinaigrette. Place tomatoes on top of croutons, and season with 1/2 teaspoon kosher salt (to encourage them to release some of their juices); let stand 10 minutes.

Remove onions from vinegar, reserving vinegar. Add onions, cucumbers, basil, and remaining croutons to bowl with tomatoes. Toss with reserved onion vinegar, remaining 3/4 cup reserved vinaigrette, and remaining 3/4 teaspoon kosher salt, adjusting amounts as desired. Divide salad evenly among 4 to 6 plates. Sprinkle with sea salt.