Caramelized Onion Tortelli in Parmesan Broth

Name: Caramelized Onion Tortelli in Parmesan Broth
Ingredients: Pasta & Filling; 4 yellow onions (about 2 pounds), halved, peeled, and thinly sliced; 30 milliliters (2 tablespoons) extra-virgin olive oil; Kosher salt and freshly ground black pepper; 2 sprigs fresh thyme; 2 sprigs fresh rosemary; 6 sage leaves; 55 grams (4 tablespoons) unsalted butter, cut into small pieces; 15 milliliters (1 tablespoon) aged sherry vinegar or balsamic vinegar; 120 grams (½ cup) whole-milk ricotta; 50 grams (1½ to 2 ounces; about ¾ cup) grated smoked mozzarella or scamorza; 300 grams (about 2½ cups) '00' pasta flour or all-purpose flour; 50 grams (about ¼ cup) semolina or semola rimacinata flour (optional; if unavailable, use the same weight in ‘00’ or all-purpose flour); 200 grams eggs (about 4 large eggs), beaten; Semolina flour or cornmeal, for dusting; Broth; 225 grams (4 to 5 large) Parmigiano-Reggiano rinds; 2 garlic heads; 1 large yellow onion; 1 large or 2 medium carrots, roughly peeled and cut into 1½-inch pieces; 2 celery stalks, trimmed, cleaned, and cut into 1½-inch pieces; 5 sprigs fresh thyme; 5 sprigs fresh parsley; 2 dried bay leaves; 5 grams (2 teaspoons) black peppercorns; Kosher salt, to taste; Parmigiano-Reggiano, for serving (optional)