Preheat the oven to 160C/325F/Gas 3. Pour the milk and cream into a pan and add the garlic, nutmeg, parsley and thyme. Season to taste and just heat through but do not allow the mixture to boil, then quickly remove from the heat.
Using a mandolin cutter, thinly slice the potatoes and sweet potatoes, being very careful of your fingers - or use the slicing attachment of your food processor as doing them by hand with a sharp knife can be a very laborious task indeed.
Butter a large ovenproof dish. Arrange a third of the potatoes and sweet potatoes in the bottom and season to taste. Add another third of both types of the potatoes in an even layer. Season to taste. Arrange the rest of the white and sweet potatoes on top in an attractive overlapping layer and pour over the milk mixture.
Cover the gratin with a piece of foil and bake for 1 hour until cooked through and lightly golden, then remove the foil and return to the oven for another 10 minutes or until the top is bubbling and golden brown.
To serve, divide the white and sweet potato gratin into portions and use as required.