Season chicken cutlets with salt and black pepper. Pour flour into a shallow dish. Press chicken cutlets into flour to coat each side, shaking to remove any excess flour.
Melt butter in a large skillet. Cook chicken in hot butter until browned, 3 to 5 minutes per side; remove from skillet and set aside.
Mix chicken broth, Marsala wine, and garlic into the remaining butter in the skillet; reduce heat to low and cook until the liquid is hot, about 5 minutes. Stir mushrooms, tomato, rosemary, and basil into the liquid. Return chicken to the skillet. Place a cover on the skillet and cook until the chicken is no longer pink in the middle, about 30 minutes.