Stuffed White Mushroom Caps

Name: Stuffed White Mushroom Caps
Ingredients: 1/8 cup extra-virgin olive oil; 1 small bunch fresh thyme, tied together with a string; 1 yellow onion, peeled and finely diced; Kosher salt and freshly ground black pepper; 2 small cloves garlic, peeled and grated on a microplane; 1/2 teaspoon ground cumin; 12 ounces white mushrooms, stems lightly trimmed, all washed and thinly sliced; 1/4 cup dry vermouth; 1 cup sour cream; 1/3 cup grated Parmesan, divided; 4 tablespoons unsalted butter; 18 white mushrooms, about 1 1/2 pounds, stems trimmed slightly, washed; Salt and freshly ground black pepper; 1/2 cup dry vermouth; 2 tablespoons toasted bread crumbs; 1 tablespoon balsamic vinegar, for finishing