Combine the flour, salt, and pepper in a shallow bowl.
Heat the olive oil in a very large skillet over medium-high heat. Dredge the chicken cutlets in the flour mixture and once the oil is hot, cook the cutlets in the pan for about 2 minutes on each side until they are golden brown, and almost but not quite cooked through (they'll continue to cook in the sauce later). Transfer the cutlets to a large plate.
Turn the heat down to medium and add the garlic. Stir for just 1 minute until you can smell the garlic. Add the chicken broth and stir so that any browned bit stuck to the bottom of the pan are released into the liquid. Stir in the cream, basil, oregano and Parmesan. Bring to a simmer and cook, stirring frequently, until the sauce thickens, about 4 minutes.
Stir in the spinach and tomatoes, and simmer for another 2 minutes or so, until the spinach is wilted and everything is well combined. Tuck the chicken back in the pan, with any juices that may have collected, making sure it is at least mostly covered by the sauce. Cook for 2 more minutes until the chicken is hot and cooked through.
Either serve the chicken over the hot pasta, or transfer it to a serving dish. Sprinkle with the parsley, and serve hot with extra Parmesan passed on the side.