1 teaspoon fine sea salt, divided, plus more for water
2 medium yellow squash, cut lengthwise into (1/4-inch-thick) slices
2 medium zucchini, cut lengthwise into (1/4-inch-thick) slices
4 red and yellow bell peppers, cored and quartered
2 large carrots, cut diagonally into (1/4-inch-thick) slices
1/2 medium eggplant (about 1/2 pound), cut into (1/3-inch-thick) rounds
1/4 cup extra-virgin olive oil
1/4 cup red wine vinegar
2 teaspoons Dijon mustard
1 1/2 teaspoons sugar
1 teaspoon finely chopped fresh thyme
1 small shallot, finely chopped
1/4 teaspoon ground black pepper
1 1/4 teaspoons unflavored powdered gelatin
1 cup low-sodium vegetable broth, divided
1/2 cup grape tomatoes, halved
8 large fresh basil leaves, divided