In a pan, combine mushrooms, onion, and olive oil. Stir often over medium-high heat until mushrooms are juicy, about 4 minutes, add parsley.

Over high heat, crumble meats with a spoon and stir often until well browned, 10 to 15 minutes.

Add mushroom mixture, thyme, vinegar, tomato paste, tomato sauce, and stock, stir until boiling. Reduce heat and simmer, stirring often, until most of the liquid has evaporated, about 30 minutes.

Spoon the cheese sauce into a shallow casserole and spread evenly over bottom. Arrange 1/4 of the pasta evenly over the sauce to cover as much of the casserole bottom as possible. Spoon 1/3 of the meat sauce over pasta in casserole and spread level.

Drizzle meat sauce with about 1/2 cup cheese sauce and sprinkle with about 1/4 cup cheese. Cover cheese with another 1/4 of the pasta and top with another 1/3 of the meat sauce, 1/2 cup cheese sauce, and 1/4 cup cheese.

Arrange a third layer of pasta over cheese and cover with remaining meat sauce, 1/2 cup cheese sauce, and 1/4 cup cheese.

Cover with the last 1/4 of the pasta and spread remaining cheese sauce over pasta to moisten evenly; sprinkle with remaining cheese and the nutmeg. Cover pan tightly with foil.

Bake at 350°C on convection oven until sauce is bubbling vigorously and pasta edges are beginning to brown (lift a corner of foil to check), about 40 minutes.

Let stand about 10 minutes; cut into rectangles and serve with a wide spatula.