Place unpeeled onions in a saucepan. Cover with water and boil 20 minutes. Drain and allow to cool. Butter a 9″x9″ baking dish. Preheat oven to 375 degrees. Peel cooled onions, removing roots and stem. Remove center, leaving a 1/2″ shell. Place shells in baking dish. Chop onion centers finely and combine 1 cup of the chopped onion with the cheddar cheese, crumbs, mushrooms, oregano & thyme. Add S&P to taste. Spoon into shells.
Cover and bake about 1 hour, until onions are tender. Meanwhile, melt butter, stir in flour, add 2 Tbsp. parsley and the milk. Cook until sauce thickens and add salt. Combine Parmesan cheese, 2 Tbsp. parsley and paprika in a bowl. Transfer onions to serving dish, pour sauce over, then sprinkle with Parmesan mixture and serve.