Add dried mushrooms to a small bowl and cover with warm water. Set aside to rehydrate, about 15 minutes. Roughly chop the mushrooms and reserve the water. Meanwhile, cut leeks in half lengthwise then thinly slice. Wash well then dry.

Heat 2 tablespoons oil in a dutch oven or heavy-bottomed pot over medium heat. Add half the mushrooms in an even layer and cook, undisturbed, until lightly browned on one side, about 2 minutes. Stir and cook until browned on all sides, another 2-3 minutes. Adjust heat to avoid burning. Move the mushrooms to the side of the pot then add 1 tablespoon oil and the remaining half mushrooms. Continue to cook, stirring occasionally, until all mushrooms are well browned, another 3-4 minutes. Remove mushrooms to a bowl and set aside. 

Add remaining 1 tablespoon oil to pot and stir in leeks. Cook, stirring occasionally, until wilted and lightly browned, 2-3 minutes. Sprinkle with ½ teaspoon salt and the black pepper. Continue to cook until very soft, another 2-3 minutes .Stir in shallot (or onion), garlic cloves, and fresh thyme; cook until fragrant. 

Add reserved mushrooms, chopped rehydrated dried mushrooms, and stock. Carefully pour in the mushroom soaking liquid, being careful not to pour in any dirt from the bottom of the bowl. Sprinkle with remaining ½ teaspoon salt. Bring mixture to a boil then reduce heat to a low simmer and cook until tender and flavorful, about 20 minutes. Stir in heavy cream and serve immediately.