In a medium pot, simmer the porcini mushrooms in the stock to soften, about 10 minutes.
In a soup pot, heat 1/4 cup EVOO over medium-high heat. When the oil begins to ripple, add the mushrooms and cook until lightly browned and tender, 12-15 minutes. Add the shallots, garlic, bay leaf and thyme; season with salt and pepper. Stir until the shallots soften, 2-3 minutes. Add the marsala, scraping the bottom of the pan. Cook until reduced by half.
Remove the porcini mushrooms from the stock, chop, then add to the pot. Pour the porcini stock into the soup pot, being careful not to add the last few spoonfuls where grit may have settled. Add 2 cups water to the pot and simmer until flavors combine, about 10 minutes. Season to taste.
In a skillet, heat a thin layer of EVOO over medium heat. Add the bread and cook until light golden and crisp.
Before serving, stir the parsley and lemon juice into the soup. Place a piece of fried bread in each soup bowl, sprinkle with a little cheese and top with soup.