Preheat your oven to 325 degrees. Butter a gratin dish or baking dish (9 by 13 inch).
2 tablespoons butter
Rinse your celery well. Tear off the biggest outer stalks, about 8-10 of them. Save the leaves on the top of the stalks. Try to scrape off the strings on each stalk. A peeler works well for this. Then cut them into 3 inch lengths. Place them in the baking dish.
1 head celery
Chop the celery heart and leaves finely and sauté with the shallot and thyme until is is starting to brown. Add vermouth and then broth and cook down until it’s about 1/2 cup liquid total.
1 large shallot finely minced, 2 teaspoons chopped fresh thyme, 1/4 cup dry vermouth, 1 cup vegetable stock
Pour that goodness over the stalks. Cover the dish with some foil and cook in oven for about 1 hour. At that point, it should be fairly soft.
Take out and turn oven up to 425. Sprinkle bread crumbs and cheese on top. Put back in the oven uncovered for another 15 minutes or so. The topping should be browned.
1/2 cup grated Parmigiano-Reggiano, 4 tablespoons bread crumbs