Heat oil in a large skillet over medium heat. Add broccoli rabe and 1 tablespoon water. Cover; cook 8 minutes, until crisp-tender, stirring occasionally. Set aside and keep warm.
Meanwhile, sprinkle salt and freshly ground black pepper, both to taste, on steaks. Heat large nonstick skillet coated with cooking spray over medium-high heat until hot. Add steaks; cook 3 minutes per side for medium-rare, or longer for desired doneness. Using a meat thermometer, check that meat has reached an internal temperature of 145º. Transfer steaks to a serving plate; keep warm.
Add mushrooms to the skillet. Cover; cook over medium-high heat, 3 minutes. Add port. Simmer, uncovered, 3 minutes, until sauce thickens slightly. Serve mushrooms over steaks; top with thyme. Season broccoli rabe with salt and freshly ground black pepper, both to taste. Serve with steaks.