Step 1

Place oven racks in upper third and middle of oven; preheat to 350°. Place cabbage on a rimmed baking sheet and drizzle with oil; season lightly with salt and pepper. Roast until tender and edges are golden, 40–45 minutes. (This is an essential first step: It draws out the excess moisture, ensuring that the cream mixture doesn’t get watery.)

Step 2

Meanwhile, bring shallots, garlic, cream, 1 Tbsp. thyme, 1½ tsp. salt, and 1 tsp. pepper to a simmer in a small saucepan over low heat. Cook, stirring occasionally, until shallots and garlic are very soft, 15–20 minutes. Let cool slightly. Transfer to a blender; blend until smooth.

Step 3

Rub the inside of a 3-qt. shallow baking dish with butter. Arrange cabbage in dish so wedges are lying on a cut side; pour cream mixture over. Bake on middle rack, uncovered, until cream thickens, 30–40 minutes. Let cool 30 minutes.

Step 4

Heat broiler. Sprinkle Gruyère and Parmesan evenly over cabbage. Broil until cheese is bubbling and gratin is deeply browned, about 4 minutes. Top with more thyme.

Step 5

Do Ahead: Gratin (without cheese) can be baked 1 day ahead. Cover and chill. Bring to room temperature before sprinkling with cheese and broiling.