Bring the milk and the stock to the boil in a pot. Remove from the heat and set aside.
Melt the butter in a saucepan and add the chopped onion. Stir and cover with a lid and sweat until the onion is cooked. Increase the heat to high, add the sliced mushroom and cook for 4-5 minutes.
Reduce the heat to low, season with salt & freshly ground black pepper, add the flour and stir and cook for 2-3 minutes.
Slowly add the stock and milk to the mushroom stirring all the time. Increase the heat and bring to the boil.