Step 1

Preheat oven to 400°F. Trim dark-green tops and root ends from leeks and discard; halve lengthwise. Remove thick, tough outer layers (2 to 4 total, depending on size), discarding or reserving for another use. Thoroughly wash and drain leeks, keeping them intact. Arrange in a snug single layer, cut sides up, in a broiler-safe baking dish or skillet.

Step 2

In a small saucepan, boil wine 30 seconds. Add broth and return to a boil; season generously with salt and pepper. Pour mixture over leeks, then sprinkle with butter and thyme. Cover dish with parchment-lined foil.

Step 3

Roast 45 minutes. Uncover and continue roasting until leeks are very soft and broth mixture is reduced by half, 20 to 22 minutes.

Step 4

Switch oven to broil. Sprinkle leeks with cheese. Broil 6 to 8 inches from heating element until bubbly and browning in places, 3 to 5 minutes. Serve warm, with some of braising liquid.