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Bake the gratin the day before; reheat, covered in foil, at 200°C, fan 180°C, gas 6 for 20-25 minutes.
Preheat the oven to 200°C, fan 180°C, gas 6. Pour the cream and milk into a pan. Add the honey, a generous grating of nutmeg, the thyme, bay and ½ teaspoon of salt. Bring to simmering point, then leave to infuse for 10 minutes. Strain into a bowl, discard the flavourings and return the liquid to the cleaned pan.
Slice the parsnips lengthways, into thin strips, using a mandolin or a very sharp knife. Alternatively, slice into thin discs using a food processor. Add the parsnips to the pan, stir to coat in the creamy mixture, cover with a lid and simmer for 2-3 minutes. Pour into an ovenproof dish and cover with foil. Place on a baking tray and bake for 15 minutes. Remove the foil and bake for a further 25-30 minutes until browned and the parsnips are tender.