Sprinkle the chicken breasts with salt and set aside. While that sits, prep everything else: Combine the flour and pepper on a large plate or shallow dish; chop the shallot and mushrooms; combine the wine, broth, and heavy cream in a liquid measuring cup.
3 boneless skinless chicken breasts, 1 teaspoon kosher salt, ½ cup all-purpose flour, ½ teaspoon ground black pepper
Heat your electric skillet to medium-high heat. Add 2 tablespoon of olive oil and 2 tablespoon of butter. While it is heating, dredge each piece of chicken in the flour mixture very lightly and shake off the excess.*Note, you can also make this in a 12 inch skillet on the stove. In this case, cook the chicken in two rounds with 1 tablespoon oil, 1 tablespoon butter and three breasts at a time to avoid overcrowding the pan. 2 tablespoon olive oil, 2.01 tablespoon butter
Add the chicken to the hot pan and cook undisturbed for 3-4 minutes on each side, until golden brown and mostly cooked through. Remove and set aside.
In the now empty skillet, add the last tablespoon of butter. Once melted, add the mushrooms and saute for 4-5 minutes, stirring often and scraping up any brown bits from the bottom of the pan. You want the liquid to evaporate and the mushrooms to turn golden brown.
0.99 tablespoon butter, 8 oz bella mushrooms
Add the shallot, garlic, and rosemary and cook for another 1 minute, stirring often. Then add the marsala, chicken broth, and cream. Bring the mixture to a boil, then reduce the heat until it is simmering rapidly. Simmer the sauce until it is slightly thickened and has gotten a little darker in color, about 10 minutes (don't give up on it... it thickens the most near the end).
1 medium shallot, 2 teaspoon garlic, ½ teaspoon dried rosemary, ¾ cup dry Marsala wine, ¾ cup chicken broth, ¾ cup heavy cream
Return the chicken to the skillet and continue simmering the sauce for another 1-2 minutes, until everything is warm and the sauce is thickened a little further. Turn the chicken around a few times to coat in the sauce, then serve warm.