Put the flour, salt, and pepper in a gallon-size zip-lock bag. Shake to mix. Add the chicken, seal the bag, and toss until all of the chicken is evenly coated.
In a large skillet (cast-iron or stainless steel for best browning), warm the olive oil and 2 tablespoon of the butter over medium heat. When the butter melts and its foaming subsides, add the chicken. Cook until the chicken is golden brown but not cooked through -- about 3 minutes per side. Remove the chicken to a plate.
Add the remaining 2 tablespoons of butter to the skillet. Then stir in the onion, mushrooms, garlic paste, and a sprinkling of salt and pepper. Saute over medium-low heat until the mushrooms begin to brown -- about 4 minutes. (If you are using diced fresh garlic, add it after the mushrooms have browned.)
Add the broth, Marsala wine, heavy cream, and Italian seasoning to the skillet. Bring to a boil over high heat while stirring from time to time. Then lower the heat, and let the sauce simmer gently until it reduces and begins to thicken -- 8-10 minutes. Return the chicken to the skillet, spoon some of the sauce over each piece, and cook just until the chicken achieves 165°F when tested with a digital thermometer -- 5-10 minutes. Do not over-cook the chicken!
Serve each chicken piece on a bed of mashed potatoes (or rice, or pasta), and spoon some of the sauce over the top. Enjoy!