Heat the olive oil in a large cast iron skillet over medium heat.
In a small bowl, combine the 1/4 cup of flour, 1/2 tsp of sea salt, and 1/2 tsp of black pepper.
Cut the chicken breasts in half lengthwise.
Dredge the chicken breasts in the flour mixture and carefully place the chicken into the hot skillet.
Sear the chicken for 4-5 minutes per side or until the internal temperature is 165℉.
Remove the chicken from the skillet to a plate and tent with foil.
Melt the butter in the skillet.
Add the mushrooms, diced shallot, and minced garlic. Sauté until cooked through and all of the moisture is absorbed.
Stir in the 1/2 cup of flour and continue cooking for 3-4 minutes.
Deglaze the pan with the marsala wine, stirring continuously.
Add the chicken broth, sea salt, black pepper, and heavy cream.
Bring the sauce to a simmer. Simmer for 8-10 minutes or until the sauce is thickened.
Return the chicken to the skillet and spoon the sauce on top of the chicken.
Remove from the heat and serve immediately.