Preheat the oven to 350 F.
Wipe the mushrooms clean with a damp towel.
Remove the stems and discard them.
Scrape out the gills and any remaining stems with a spoon, making deep cups.
Stir the crabmeat, scallions, thyme, oregano, savory, and pepper together in a small bowl.
Stir in 1/4 cup Parmesan cheese and the mayonnaise, mixing with a fork until combined.
Fill the mushroom caps with rounded teaspoonfuls of the filling, and place them in an ungreased shallow baking dish.
Bake for 15 minutes.
The filled mushrooms may be covered and refrigerated overnight.
Reheat them at 350°F for 7 to 10 minutes, or until hot.
Sprinkle the tops with additional Parmesan cheese and paprika.
Place the mushrooms under the broiler for 2 minutes, or until lightly browned.