Place rack in middle of oven and preheat to 400F. Brush a baking sheet lightly with oil.
Wipe any grit from mushrooms with a damp cloth or paper towel. If portobellos have stems, carefully snap them off; trim and chop stems. Use a teaspoon to scrape gills from caps; discard gills.
With motor of food processor running, drop garlic into feed tube and finely chop. Scrape down sides and add onion, mushroom stems (or button mushrooms; see note below), cereal, parsley, oil, 1 tablespoon cheese, oregano, salt, and pepper to taste.
Brush mushroom caps lightly with oil. Place on baking sheet. Divide filling among caps. Sprinkle remaining cheese on top.
Bake until mushrooms are easily pierced with a skewer, 13 to 15 minutes. Set under the broiler until tops are lightly browned, 1 to 2 minutes. Serve as an entrée or side dish.