Remove stems from mushrooms and set aside for another use.  Set mushroom caps aside.  In medium bowl, stir together eggs, crumbs, cheese, onion, wine, butter, parsley, and garlic salt until well combined.  Fill each mushroom cap with 1 rounded tablespoon of egg mixture.  Place filled caps on lightly greased baking sheet.

Bake in preheated 450° F oven until heated through, about 8 to 10 minutes.  Sprinkle with paprika, if desired.

*To hard-cook:  place eggs in single layer in saucepan.  Add enough tap water to come at least 1 inch above eggs.  Cover.  Quickly bring just to boiling.  Turn off heat.  If necessary, remove pan from burner to prevent further boiling.  Let eggs stand, covered, in the hot water, 15 minutes for Large eggs (about 18 minutes for Extra Large eggs and about 12 minutes for Medium).  Immediately run cold water over eggs or place them in ice water until completely cooled.

To remove shell:  crackle it by tapping gently all over.  Roll egg between hands to loosen shell.  Then peel, starting at large end.  Hold egg under running cold water or dip in bowl of water to help ease off shell.

Kitchen-Tested Recipe from the American Egg Board