Clean the mushrooms with a brush, remove the stems of button mushrooms and thinly slice all mushrooms.
In a large pan or skillet, heat olive oil over medium-high heat. Add shallots and cook until tender, stirring occasionally, for about 10-15 minutes. Add the garlic, stir and cook for another 30 seconds, until it's aromatic.
Add the mushrooms and cook until they release all the liquid, stirring occasionally.
Add the salt, vegetable stock and thyme and cook for 5-10 minutes, until most of the liquid evaporates. Mix in cream and cook for another minute.
Remove mushrooms from the stove, stir in the parsley. Taste and add a pinch of salt and a grind of black pepper, or more to taste.