Clean the mushrooms and cut them into 2.5mm [0.1 inch] thin slices. Put the cream, 1 crushed garlic clove, rosemary sprig and milk into a small saucepan. Slowly heat up until everything is just boiling. Turn off the heat, season and leave on the side to infuse. Pre-heat the oven to 180°C/350°F/Gas 4.
Heat the butter in a large frying pan. Add finely chopped shallots. Fry gently for a few minutes until soft.
Add the sliced mushrooms, white wine and finely chopped rosemary.
Cook covered under medium heat for 5 minutes. Carry on cooking uncovered for around 8 minutes until the mushrooms are done. Season to taste.
In the meantime cut the potatoes into 2.5mm [0.1 inch] slices. Put them on a clean cloth and pat dry.
Grease a gratin dish generously with butter. Rub the second garlic clove all over the gratin dish.
Layer half of the potatoes at the bottom of the gratin dish. Season with salt, pepper and nutmeg.
Add the mushrooms and their juices (if any) on top.
Spread 5 Tbsp of the cream and milk mixture on top of the mushrooms.
Layer the second half of the potatoes on top of the mushrooms. Season with salt, pepper and nutmeg.
Add the rest of the cream and milk mixture (rosemary sprig removed) on top. Sprinkle with grated cheese all over.
Cook in the oven for 45 - 60 mins until the potatoes are cooked and gratin is golden.