Boil the pasta until just tender. Drain well, cool in ice-cold water, drain again, and place in a bowl.
Preheat the oven to 350 degrees F.
Lightly butter a 9" x 13" casserole. Place the butter and oil in a pot set over medium heat. Add the onion, celery, bell pepper, zucchini, and garlic and cook 3 to 4 minutes. Mix in the flour and oregano and cook 2 minutes more. Slowly whisk in the milk. Bring to a simmer, stirring frequently, and simmer until the sauce thickens, about 3 to 4 minutes. Stir in the cheese, salt and white pepper.
Add the sauce, peas, corn and green onion to the pasta and mix to combine. Spoon into the casserole dish; sprinkle with Parmesan cheese. Cover and bake 20 minutes. Uncover and bake 10 to 15 minutes more, or until golden and bubbling.