Photograph: Martin Poole
Preheat the oven to 200°C, fan 180°C, gas 6. Put the mushrooms in a roasting tin and drizzle over the olive oil. Roast for 20 minutes until tender, then slice thinly. Reduce the oven temperature to 180°C, fan 160°C, gas 4. Lightly grease a 28 x 21cm ovenproof dish with the butter.
Put the sliced potatoes in a large saucepan with the cream and milk and add a generous pinch of salt.
Bring to the boil, reduce the heat and cover with a lid. Simmer, stirring regularly, for about 10 minutes until slightly thickened. Taste the sauce and add more salt if necessary.
Spoon a third of the potato mixture into the buttered dish, scatter over half the sliced mushrooms, some of the chopped sage and season with black pepper. Repeat with another layer of potatoes and mushrooms, seasoning in between. Finish with a layer of potatoes and the pecorino.
Bake in the preheated oven for 1 hour or until cooked through - it will be creamy, golden and bubbling.