Trim any excess fat from the chicken breasts and slice in half lengthwise. Season both sides of the chicken breasts evenly with 1/2 teaspoon kosher salt and 1/2 teaspoon freshly ground black pepper, then dredge each breast in the flour, shaking off any excess.
Heat 2 tablespoons of the canola oil in a large skillet over medium-high heat. Add 4 pieces of the chicken and cook for 2-3 minutes per side. Transfer to a platter or sheet pan and cover with foil. Continue with the remaining chicken (add another tablespoon of oil if needed) and and add the cooked chicken to the platter when done.
Melt 3 tablespoons of the butter in the skillet and add the mushrooms and shallot. Sauté over medium heat, stirring occasionally, until the shallots are wilted and the water from the mushrooms has evaporated, about 10 minutes. Add the marsala wine and the chicken stock. Bring to a boil and season with remaining 1/2 teaspoons of kosher salt and black pepper. Stir in the remaining butter and cook over medium heat until reduced by half. Add the chicken and simmer for 5 minutes. Sprinkle with parsley and serve with egg noodles, pasta, polenta, mashed potatoes, or over rice.
Marsala wine is totally unique, with a deep, sweet flavor, so If you don't have Marsala, try brandy, sherry, or Madeira, but know that the taste will be different.When reduced, the alcohol evaporates so all that's left is it's delicious flavor. But, if you want a non-alcoholic substitute for Marsala wine, try grape juice or this combination of grape juice, vanilla, and sherry vinegar.