Preheat the oven to 160C/140C fan. Peel the potatoes then cut them into 2 millilitre slices, using a mandolin or kitchen knife.
Put the milk and cream into a saucepan with the garlic, shallot, rosemary, thyme and bay leaf. Warm very gently for 5 minutes to infuse the flavours, don’t let it come to a boil - then pick out the bay leaf and herb stalks, and put to one side.
Mix the cheddar/mozzarella mix and gruyere together. Lightly butter the inside of the gratin dish. Place a thin layer of purple potato slices on the bottom of the dish, followed by a thin layer of cheese. Spoon over the milk mixture, until just covered, then add a layer of sweet potatoes. Carry on layering in thin layers to create as many overall layers as possible. Finish with the milk mixture and a big handful of cheese. Place a few sprigs of herbs on the top then bake, uncovered, for 1 hour.
After 1 hour, insert a thin knife into the gratin to check it’s cooked - it should be soft all the way through. Leave to stand for 10 minutes before serving.