Use side burners or preheat grill. Heat oil in a medium saucepan over medium high heat. Add onions and garlic and cook until soft. Add mushroom stems and cook until golden brown. Remove from heat and add bread crumbs, parsley, hot pepper sauce and cheese. Mix until well combined (if mixture looks too dry, add more olive oil.) Season the mixture with salt and pepper to taste. Fill the mushroom caps with the mixture and brush the entire mushroom with more olive oil. Grill over medium heat until tender.