Pound the chicken to ½” thick.
Combine the spinach with the parmesan cheese until well mixed.
Stuff and roll the chicken with the spinach and parmesan mixture, and secure each with a toothpick.
Combine ¼ cup flour with the salt and black pepper in a large bowl until well mixed.
Dredge the chicken in the flour mixture and transfer to a plate.
Heat the olive oil in a wide oven-proof saute pan over medium heat until shimmering.
Add the dredged chicken and sear, turning carefully to brown each side.
Remove the chicken from the pan and set aside.
Add the remaining butter to the pan and heat until melted.
Add the remaining 2 tablespoons of flour to the melted butter, whisking until smooth.
Slowly whisk in the chicken broth and marsala wine.
Preheat the oven to 350*F.
Add the mushrooms and chicken and bring the sauce to a simmer, cooking 10-12 minutes until the mushrooms have started to soften and the sauce is thickening.
Top with cheese and place the pan in the oven until the cheese has melted, about 8 minutes.
Serve hot.