In a large frying pan or 3.5 quart braiser, heat the olive oil on medium heat; add the shallots, onion and garlic and cook until tender. Remove from the pan into a bowl; set aside.
Coat the chicken in the flour and salt and pepper (using a Ziploc bag to shake the chicken in). In the same large pot over medium-high heat, add 1 tablespoon of oil and saute half the chicken for 1 to 2 minutes per side until lightly browned. Remove to a plate and keep warm. Repeat with a second tablespoon of the oil and the remaining chicken, removing to the separate plate to keep warm.
Add the remaining tablespoon of oil to the skillet and stir in the mushrooms. Cook for 5-6 minutes, until tender. Off heat, add in the marsala and cook for 1 minute, scraping any browned bits from the skillet. Pour the sauce into a separate pan.
Add the chicken back to the pan, placing the onion mixture on top.
Next, add the cornstarch to 1/4 cup cold water, and whisk until smooth. Pour into the marsala sauce/mushrooms and heat on high, stirring until thick. Add the melted butter; stir. Add the sour cream; stir.
Pour the marsala sauce over the chicken, onions, and mushrooms in the pot. Bring the chicken marsala to a boil, then gently simmer, covered, for 15 minutes.
Meanwhile, prepare pasta following package directions, about 11 minutes.
Garnish the chicken with chopped parsley. Serve over cooked pasta.