Bring a large pot of salted water to a boil.

As vegetables are cooked, transfer to a paper towel-lined sheet tray and set aside.

In a 9x13-inch dish, whisk together oil, vinegar, mustard, sugar, thyme, shallot, 1/2 teaspoon of the salt and black pepper.

Add vegetables 1 at a time, coating well and arranging them in groups in the dish. Cover and set aside at room temperature for 1 hour.

Line an 8-inch loaf pan with plastic wrap, allowing extra to hang generously over the long sides.

Sprinkle gelatin over 1/4 cup of the broth in a medium bowl and set aside for 5 minutes.

Meanwhile, in a small pot, bring remaining 3/4 cup broth and remaining 1/2 teaspoon salt to a boil.

Pour hot broth over gelatin mixture and stir until dissolved.

Pour 1/4 cup of the broth mixture into the pan.

Arrange tomatoes in the bottom, cut-sides down, and top with half of the basil.

In layers, arrange half of the squash, zucchini, peppers and carrots, allowing each vegetable to make a complete layer, and spooning some of the gelatin mixture generously over the top of each layer

Arrange all of the eggplant and remaining basil over the top to make 2 more layers and then repeat with remaining vegetables.

Pour any remaining broth mixture over the top and gently shake and tap the pan to distribute.

Fold over plastic wrap to cover terrine, and arrange in a shallow dish to catch any drips.

Add a few small, evenly distributed weights to the top to gently press down on the vegetables (a rectangular plate with 2 cans on top, for instance).

Chill until firm, about 8 hours or overnight.

Gently loosen edges of terrine with a small knife and then carefully invert onto a platter; remove and discard the plastic wrap.

Using a very sharp knife, cut into slices and serve.