In a large skillet, heat the EVOO over medium-high heat. Add the bell peppers, mushrooms, oregano and 1 tsp. salt; cook until the vegetables are browned on the edges, about 10 minutes.
Add the tomatoes, then fill the can with 1 cup hot water and swish to collect any remaining sauce; add to the skillet. Bring to a simmer, partially cover and cook until the sauce is thickened and the peppers begin to break down, 20 to 25 minutes.
meanwhile, warm a large cast-ion skillet over medium heat until hot. Season the steaks with 1/4 tsp. salt, then add to the pan and sear, turning once, until cooked to the desired doneness, about 10 minutes for medium-rare. Transfer the steaks to a platter and let rest for a few minutes while the sauce finishes cooking.
To serve, top the steaks with the pepper sauce.