In a medium stock pot add the water, thyme, bay leaves and garlic cloves. Bring to a simmer together with all of the stalks from the shiitake mushrooms and one of the largest shiitake mushrooms.
In a large skillet add 2 tbsp pf the olive oil and saute half of the clean leeks with a pinch of sea salt for about 10 minutes. Slice the shiitake mushrooms and add them to the skillet with the leeks.