Rub the beef fillets with salt and freshly ground black pepper and brush with two tablespoons of the oil. Heat a frying pan until smoking and add the steaks, frying for 3-4 minutes on both sides (for rare), or until cooked to your liking. Transfer to warm serving plates to rest.
Reduce the heat, add the remaining oil to the pan and fry the shallots and the garlic for 2-3 minutes, or until they begin to soften. Stir in the morels and fry for 1-2 minutes, then season with salt and freshly ground black pepper.
Pour in the wine and stir in the chopped thyme leaves, then leave to simmer for 5-6 minutes, or until the liquid has thickened.
Pour the mushroom and red wine sauce over the steaks and serve.