1.Heat oil in medium frying pan; cook onion, stirring, until soft. Stir in half the parsley. Add cheese and eggs to pan; cook over low heat, covered loosely, about 8 minutes or until edges are set.
2.Preheat grill (broiler).
3.Place pan under hot grill (shielding handle with foil, if necessary) until browned lightly and just set. Invert onto cutting board.
4.Meanwhile, heat butter in small frying pan; cook garlic and mushrooms, stirring, until just tender; stir in remaining parsley.
5.Cut frittata into 16 wedges, arrange on a serving platter. Top half the wedges with the mushrooms and half with artichokes and capsicum.