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Place the cream, onion or shallot and the thyme sprig into a small pan. Slowly heat to just below boiling point, then remove from the heat and leave to cool. Strain, discarding the onion and thyme.
Heat oven to 160C/fan 140C/gas 4. Rub the bottom and sides of a gratin dish measuring about 20cm x 30cm with butter. Peel the parsnips and trim the ends. Peel and scoop the seeds out of the squash. Thinly slice the vegetables.
Layer the parsnip and squash in the dish, pour over the infused cream, then scatter with the thyme leaves and gruyère. Bake for 1 hr until golden and a fork slides easily into the veg.