1. Preheat oven to 375 degrees, with rack in upper third. Cut each head of celery in half lengthwise, and peel larger stalks with a vegetable peeler. Trim 1/4 inch from bases (keeping heads intact), then trim tops so each half is about 12 inches long. Arrange celery in a single layer, cut-sides up, in a 9-by-13-inch baking dish. Season generously with salt and pepper; scatter with thyme and dot with butter. Pour in broth and oil.

2. Cover with parchment-lined foil. Bake until celery is knife-tender, 40 to 45 minutes. Turn oven to broil; remove foil. Spoon juices over celery and broil until lightly charred in spots, 5 to 10 minutes. Serve.