Position rack in upper third of oven; preheat to 450°F.
Cut 2 unpeeled sweet potatoes crosswise into 1-inch-thick rounds; transfer to a large bowl.
Add 2 tablespoons melted butter, 2 tablespoons oil, 1 tablespoon herbs, ½ teaspoon salt and ½ teaspoon pepper; toss to coat.
Arrange the sweet potatoes in a single layer in a 9-by-13-inch metal baking pan. (Don’t use a glass dish, which could shatter.)
Roast, flipping once, until browned, about 35 minutes.
Whisk chopped garlic into 1 cup broth; carefully add the broth mixture to the pan.
Sprinkle the tops of the sweet potatoes with 3 tablespoons Parmesan.
Continue roasting until the broth has mostly been absorbed and the sweet potatoes are very tender, 12 to 15 minutes more.
Transfer to a serving platter; drizzle with the remaining butter mixture from the pan.
Sprinkle with more Parmesan, if desired.
