Place grouper and blade and bowl of food processor, in the freezer to chill for 20 minutes. Meanwhile, in a small skillet, melt butter over medium heat and cook the green onions until just wilted. Set aside to cool to room temperature. Remove grouper and food processor pieces from the freezer.
Place grouper in the processor bowl and puree on high about 1 minute. Scrape down the bowl with a rubber spatula. Add egg and process the mixture until smooth and shiny. Scrape down the bowl again and add salt, Dijon mustard, Tabasco, and Worcestershire. Process until incorporated. With the machine running, add heavy cream in a slow, steady stream until incorporated.
The mixture should be light and fluffy. Preheat oven to 425 degrees F. Fold crab and green onions into the fish mousse. Place four 3-inch metal ring molds on a lightly oiled nonstick ovenproof pan and fill with the crab mixture. Sauté cakes over medium heat until lightly browned on each side, about 3 minutes per side.