Cook the pasta in boiling salted water until al dente. Rinse under cold water and oil lightly. Set aside.
In a skillet, brown the mushrooms, onion and garlic in the oil approximately 10 minutes. Season with salt and pepper. Deglaze with the vinegar and water. Adjust seasoning. Set aside.
With the rack in the middle position, preheat the oven to 190 °C (375 °F).
In a 33 x 23-cm (13 x 9-inch) baking dish, spread a quarter of the sauce. Cover with a layer of pasta. Add another quarter of the sauce and 150 ml (2/3 cup) of cheese. Cover with another layer of pasta. Add the mushroom mixture and 150 ml (2/3 cup) of cheese. Cover with a layer of pasta. Add a quarter of the sauce and 150 ml (2/3 cup) of cheese. Finish with the remaining noodles, sauce and cheese.
Bake for approximately 45 minutes then brown under the broiler. Let stand for 5 minutes before serving.