In a bowl, combine eggs, milk and rice. Stir in parsley, butter, onion, celery salt and salt. Pour into a greased 2 quart baking dish; sprinkle with cheese. Set dish in a 13x9x2 inch pan; add 1 inch of hot water to pan.
Bake at 350 degrees for 50-60 minutes or until a knife inserted in the center comes out clean.