Pasta with Mushrooms, Chianti Style (Pasta al Funghi alla Chiantigiana)

Sauce
1 ounce dried porcini mushrooms
2 1/4 cups hot water
5 tablespoons tomato paste
8 ounces cremini mushrooms
1 cup coarsely diced red onion
2 medium cloves garlic, chopped
1/2 cup chopped parsley, divided
2 tablespoons extra virgin olive oil
1/2 cup Chianti or other dry red wine
1/2 to 3/4 teaspoon salt
1/2 teaspoon black pepper

Pasta
5 quarts water
2 teaspoons salt
3/4 pound dried fettuccini
1/2 cup pasta
1 tablespoon unsalted butter (optional)
1/2 cup coarsely shredded Parmesan cheese (optional)

Put the dried porcini mushrooms in a bowl and add 2 1/4 cups hot water. Place a small plate on top to keep mushrooms from floating and set aside 30 minutes. Drain, saving 2 cups liquid.

Rinse mushrooms briefly and press in paper towels to remove excess water. Strain the mushroom liquid through a paper towel-lined sieve. Put tomato paste in a bowl and whisk in a little mushroom liquid until smooth. Then add remaining liquid, mixing well. Set aside.

Trim stems from cremini mushrooms and wipe caps with a damp paper towel. Slice thinly and set aside. Put reconstituted porcini mushrooms, red onion and garlic on a cutting surface and chop together coarsely. Add half of parsley.

Heat olive oil in a 3 1/2 quart pan set on medium heat. Add fresh mushrooms and chopped vegetable mixture; saut