In a large skillet, heat the EVOO, 5 turns of the pan, over medium to medium-high heat. Add the portobello mushrooms and cook until tender, about 12 minutes. Set the skillet aside.
In a saucepan, simmer the dried porcinis in the vegetable broth until softened, about 10 minutes. Using a slotted spoon, transfer the porcinis to a cutting board. Chop and set aside. Pour the broth into a bowl, discarding any grit at the bottom of the pan; wipe out the pan. Return the broth to the pan, add the polenta and stir until thick, about 2 minutes. Stir in the cheese and pepper. Keep warm.
Add the marsala to the skillet with the portobellos; season with salt and pepper. Stir in the reserved chopped porcinis.
Ladle the polenta into bowls. Top with the mushrooms and parsley.