Dice the onion
Cut the mushrooms into small parts
Wash, dry and cut very fine the dill and the parsley
Prepare the washed thyme and sage leafs
Place the butter or olive oil in a pan of appropriate size and heat up
Add the diced onion, first on medium fire for 3-5 minutes while often stirring; then simmer on low for 30 minutes. Ensure the onions remain yellow and do not become black or burned
Add the thyme and sage leaves
Then add the mushrooms and first on medium heat smother them followed by a slow simmer for 30 minutes. The mush rooms will release their juices.
Add the parsley and the flour, mix with a whisk
Add the milk at medium heat, continuously stir until the mixture becomes very viscous. Put heat on low and wait for a few minutes, while stirring.
Add so much of the broth that the mixture becomes more fluid, but remains thick. Let the mixture cook for at the least 5 minutes and if needed let some of the liquid steam off, all the time vigorously stirring.
Bring to taste with pepper and salt. The mixture should be thicker than an average bechamel based sauce.
Let cool down with a lid on and heat up, just before serving the dish