Position a rack in the upper third of the oven and preheat the broiler.
Toss the tomatoes, oil, thyme and celery in a large bowl. Season with salt and a few grinds of pepper. Transfer to a baking dish and broil until browned on the edges, 15 to 18 minutes. Toss with the walnuts and lemon zest. Serve topped with the shaved Parmesan.
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