Bring a pot of lightly salted water to a boil and cook the zucchini whole until they start to become tender, about 10 minutes. Drain the zucchini and set aside to cool. Once cool slice the zucchini in half lengthwise and scoop out the center flesh, leaving a 5mm thick shell around the entire zucchini. Chop the scooped-out zucchini flesh.
Melt the butter in a large frypan over medium heat. Cook and stir the mushrooms and sweet red capsicum until tender and the mushrooms release their juice, about 5 minutes. Stir in the flour and oregano then stir in the reserved chopped zucchini flesh and cheddar cheese. Heat the mixture until the cheese is melted and the filling is hot. Stuff the filling into the hollowed-out zucchini; sprinkle each with about 3/4 tablespoon of Parmesan cheese.
Preheat the grill and set the oven rack about 15cm from the heat source.
Grill the zucchini until the filling is bubbling and the cheese is browned, 3 to 5 minutes.