Vegetarian Muffulettas

Name: Vegetarian Muffulettas
Ingredients: 1 cup olive oil; 10 garlic cloves; 3 thyme sprigs; 1/2 teaspoon crushed red pepper; 1 1/2 pounds eggplant, cut into 8 (1/2-inch-thick) eggplant rounds; 4 red bell peppers, halved lengthwise and seeds removed; 4 large portobello mushroom caps (14 ounce total); 2 teaspoons kosher salt; 1/2 teaspoon freshly ground black pepper; 1 cup chopped pitted Castelvetrano olives (from 1 1/4 cups unpitted olives); 1 1/4 cups jarred giardiniera (mixed pickled vegetables), chopped, plus 3 tablespoon brine from jar; 2 tablespoons drained capers; 4 round seeded crusty rolls, split; 8 sharp provolone cheese slices