In a small bowl with 1 1/2 cups, of warm water soak the dried mushrooms for 10 min. Remove the mushrooms reserving the liquid and coarsely chop. Pour the liquid through a small sieve reserving one cup. Set both aside.

Meanwhile, in a large pot add 1 Tbsp of butter and olive oil and heat over medium heat, when the butter is melted add the shallots and saute until tender, about 4 min.

Add the fresh mushrooms and 1 tsp. salt. Cook until they start to soften, 6 min. Add the dried mushrooms and continue cooking for about 4 minutes more or until the mushrooms have released their liquid and are very tender.

Add the vermouth and cook until it is evaporated for about 2 min. more. Add the reserved mushroom water from the dried mushrooms and reduce to 1/3 cup. Stir in the heavy cream and 3 Tbsp. of the herbs. Adjust seasoning with salt and pepper. Keep warm.

In a medium pot bring 4 1/2 cups of water to a boil and add cornmeal, 1 tsp. salt and stir. Cover and cook for 5 min. stirring occasionally. Whisk if needed to make it smooth. Whisk in the remaining 2 Tbsp. butter and the mascarpone. Add the parmesan and stir with a spoon.

Serve the polenta with the mushrooms on top, sprinkled with the remaining herbs and the goat cheese.