Preheat oven to 350.
Combine cornmeal with 4 cup water in 1 1/2-quart baking dish.
Add salt, pepper, and butter.
Bake, uncovered, 40 minutes. Stir and add cheese.
Bake 10 minutes more. Let stand 5 minutes.
Meanwhile, soak porcini mushrooms in 1 1/2 cup hot water until soft (about 15 minutes).
While they soak, melt butter in large skillet. Add shallot and saute. Add garlic, cook 2 more minutes.
Add fresh mushrooms. Cook 4-5 minutes or until soft.
Strain porcinis, reserving liquid. Chop. Add liquid and mushrooms to fresh mushrooms. Cover. Reduce heat to low and cook until mushrooms are completely limp, 8-15 minutes.
Uncover. Increase heat to high and cook until liquid is almost absorbed, 7-8 minutes. Stir in parsley.
Serve mushrooms over polenta.