Place steak in the freezer for 30 minutes. Slice as thin as you possibly can — almost see-through.
Heat 1 tbsp oil and 1 tbsp butter in a large heavy pan over medium-high. Add onions and capsicum. Cook 8-10 minutes until soft and lightly caramelised. Tip onto a plate.
Crank heat to high. Add remaining oil. Add the shaved beef. Toss with two spatulas, breaking up clumps. Salt and pepper generously. Cook 90 seconds — just until no longer pink.
Return onions to the pan. Toss with the beef. Reduce heat to low.
Lay cheese slices over the beef. Cover briefly with a lid or foil so cheese melts.
Split hoagie rolls down the middle, butter the inside, toast briefly under the grill.
Pile beef-and-cheese mixture into each roll. Serve immediately.