Heat oven to 425°F and position a rack in the center.
Slice the cabbage into thick slabs, keeping the core attached so the pieces hold together.
Whisk melted butter, olive oil, garlic, thyme, red pepper flakes, and half the salt and pepper.
Arrange cabbage in a 9x13-inch baking dish in a single layer. Spoon about half the garlic butter over the slabs.
Pour the broth into the bottom of the dish around the cabbage, not over it.
Cover tightly with foil and bake 25 minutes to steam and soften.
Uncover, baste with pan juices, and brush with the remaining garlic butter. Bake 20–25 minutes more until very tender and browned at the edges.
Broil 1–2 minutes if you want extra caramelized edges.
Drizzle with lemon juice, sprinkle Parmesan and parsley, and season with remaining salt and pepper. Rest 5 minutes and serve with the buttery juices.