If chicken is large, slice each breast horizontal for 2 cutlets per breast. Season both sides with kosher salt, black pepper and Italian seasoning. Dust each side with flour. Set aside.
In a large skillet over medium high heat add 2 tablespoons of the butter and the oil. Sauté chicken for several minutes on each side until golden brown and crispy (internal temp should be 165°F).
Remove chicken from pan and drain on a paper towel on a plate - keep warm, covered with aluminum foil.
Add 1 tablespoon of butter and sauté the shallots until almost translucent and add the sliced mushrooms. Cook for several minutes, stirring.
To the sauté pan over medium heat add the chicken stock, madeira and scrape the bits of cooked pieces on bottom of pan.
Add the cream, whisking to incorporate, bring to a boil and allow sauce to reduce and thicken, 2-3 minutes. Turn off heat then add the remaining 1 tablespoon of butter, stirring to incorporate. Pour sauce over chicken and serve. Garnish with chopped parsley.