Heat the butter and olive oil together.
Add the mushrooms to the pan with the thyme and season with salt and pepper.
Allow the mushrooms to fry until golden brown then add the garlic and fry until fragrant.
Whisk the cornstarch into the milk.
Pour in the cream and milk and allow to simmer gently for 5-10 minutes until the sauce has thickened and cooked through.
Season with lemon, salt and pepper and add the parsley.
