Cook pasta according to package directions (omitting salt) until tender, 8 to 10 min. Drain and set aside.
Heat an extra-large frying pan over medium. Add oil, then garlic, onion, pepper and mushrooms. Cook until onion and mushrooms start to soften, 3 to 4 min.
Crumble in meat. Stir in tomato paste, chili powder, dried oregano and salt. Cook, breaking up meat with a wooden spoon, until no longer pink, 3 to 5 min.
Add passata, cooked pasta and beans. Gently boil until heated through. Sprinkle cheese overtop. Reduce heat to medium-low. Cook, covered, until cheese melts, about 2 min.
Serve immediately or freeze for later!