Place the porcini mushrooms in a medium bowl. Pour two cups of water over the mushrooms and let them soak for 15 minutes. Drain the mushrooms, reserving the soaking water.
Heat the olive oil in a large saute pan over medium heat. Add the scallions and porcini mushrooms. Cook until the scallions are soft, but not browned, about five minutes. Add the thyme and garlic. Cook for about two minutes.
Add the white wine to the saute pan and increase the heat until the mixture begins to boil. Simmer until the wine is mostly evaporated, about 5-10 minutes.
Add the two cups of chicken broth, reserved porcini mushroom liquid, and salt. Simmer briskly until the mixture is reduced by at least half, about 30 minutes.
To finish the sauce, add the parmesan cheese and butter. Season to taste with salt and pepper.
Combine the Palmini and sauce. Place on individual serving plates and garnish with the chopped parsley and additional parmesan cheese, if desired.