Wrap corn in foil and roast in preheated oven for about 1 hour. This can be done in advance on a prep day.
Cook rotelle according to package directions. Drain and reserve 1 cup of the cooking water. Transfer pasta to a large bowl.
Meanwhile, heat oil in a large skillet over medium heat. Add corn cut from cob, zucchini and onion and saute for 3 minutes, until golden brown. Add oregano and cook 1 minute. Add broth and roasted garlic and bring to a simmer. Simmer 5 minutes. Pour mixture over pasta and toss to combine, adding cooking water, if necessary, to moisten pasta. Fold in parsley and season, to taste, with salt and black pepper. Transfer pasta to a serving platter and top with feta cheese.