Over medium heat, melt the oil and butter in a large pan or pot and sauté the onions until soft, around 3-minutes. Stir in the paprika, pepper and mushrooms and cook, stirring regularly until the liquid has cooked away, around 7 minutes. Stir in the garlic and cook for another minute.
If you are serving the mushroom stronganoff over pasta, cook the pasta in salted boiling water according to the packet instructions while the mushrooms are cooking. When al dente, strain and drizzle the pasta with a little olive oil to prevent sticking.
Reduce the heat to low-medium and stir in the Worcestershire sauce, or soy if you can't get a vegan Worcestershire. Add the stock and dairy-free milk before stirring in the Dijon mustard and nutritional yeast. Bring the mixture up to a simmer, but don't allow it to boil - we dont want the sauce to split
With a ladle, carefully remove a quarter cup of the liquid and combine it in a small bowl with the cornflour. Stir well until the cornflour is completely mixed in and return the mixture to the pot. Over low heat, continue cooking the sauce stirring regularly. The sauce will thicken as it cooks. This will only take a few minutes.
When the sauce has thickened, remove the mixture from the heat and whisk in the cream cheese until it has melted in to the sauce. Keep whisking until the cheese has absorbed fully. It's now read to serve over pasta, rice or potatoes. Season if needed.