Put the dried mushrooms in a bowl and pour in 2 cups of boiling water, let when soak until soft, about 15-20 minutes. Drain and chop them roughly. Reserve the soaking water.
Put oil in a large skillet over medium heat, when hot, add the soaked and fresh mushrooms and sprinkle with salt and pepper. Cook, stirring occasionally, until the mushrooms are tender, 10-15 minutes. Add wine and let it bubble away for 1 minute, then stir in garlic, parsley, and a cup of reserved soaking water. Cook until the liquid thickens a bit, 1-2 minutes, taste and adjust the seasoning. Turn off the heat.
Cook polenta following directions on the package.
Serve polenta topped with mushrooms and Puopolo Casalingo, garnish with remaining parsley.