Brush the mushrooms or wipe with wet tissue to remove any patches of dust or dirt.
Scrub the mushroom stems if necessary and cut off the roots.
Cut the mushrooms into quarters or slice.
Sauté each kind of mushroom separately in olive oil over a high heat. Stir frequently until the mushroom water evaporates. Place the sautéed mushrooms in a colander and continue the second batch.
Finish the mushrooms
Melt the butter in the pan over medium heat, add the garlic and thyme and cook for a minute.
Add the sautéed pre-cooked mushrooms in the pan.Season with salt, pepper and chopped parsley.
Prepare the soft polenta
Bring the milk, stock, saffron threads, olive oil, and salt to the boil.
Reduce the heat and gradually whisk in the polenta. Keep whisking constantly until thickened and cooked. If the grains are still firm add a little water and continue whisking on the heat until soft.
Remove from the heat, add the butter, grated parmesan and stir until well combined. Season to taste and serve immediately.