Place chicken breasts on a cutting board and cover with plastic wrap. Use the flat side of a meat tenderizer to flatten the chicken breasts evenly to about a half inch thickness.
Place flattened chicken breasts in a zip-top bag with flour, salt, and pepper. Shake to coat chicken with flour mixture.
Heat Instant Pot (6 qt.) to Sauté and add oil. When oil shimmers, add chicken and cook for about 4 minutes on each side until golden brown. You may need to do it in batches. The chicken does not need to be fully cooked. Remove chicken to a plate.
Add prosciutto and mushrooms to Instant Pot and cook until prosciutto is crispy and mushrooms are browned. Add Marsala wine and chicken stock and scrape the brown bits off the bottom of the pan.
Add the chicken back in and settle it down into the liquid.
Put cover on (make sure vent is turned to “seal”). Set Instant Pot to Pressure Cook or Manual (high pressure) depending on your model, for 10 minutes. When the timer goes off, quick release the pressure. Use an instant read thermometer to ensure chicken has an internal temperature of 165°F.
Stir butter into sauce until melted.
Serve chicken topped with mushrooms, pan sauce, and fresh parsley.
Timesaver Hint: Buy chicken cutlets (you won't have to pound them). Another alternative is to cut the chicken into bite-size pieces before sautéing it.
White button mushrooms or baby bella mushrooms are good choices.
If you prefer, substitute bacon or pancetta for the prosciutto, or omit it for a lower calorie, lower sodium option. The butter can be omitted, too.
Serve with pasta, noodles, rice, or mashed potatoes.