First heat 2 tablespoons of olive oil and let the onion, carrot and celery sauté gently until just transparent. Add the mince and stir over a brisk heat for a few minutes. Put in the garlic, tomato purée and then the wine, water and bouquet garni. Bring to the boil, then turn down the heat and allow to cook for 10 minutes. In a separate pan sauté the mushrooms in enough oil to prevent them sticking to the pan.
Peel the potatoes and slice in ⅛-inch-thick slices. Steam until just tender. In a large ovenproof dish put a layer of the ragu, then a layer of the béchamel sauce and then the field mushrooms. Arrange the potato slices on this, seasoning as you go. Cover with the rest of the ragu and pour over the remaining béchamel sauce. Sprinkle with the Parmesan and cook at gas mark 6/400°F/200°C for 20–25 minutes until the cheese is bubbling.