Chill the shrimp along with the bowl and blade of a food processor in freezer for about 30 minutes. Sauté the scallions in 1 tablespoon butter until just wilted. Set aside to cool.
Place the shrimp in the processor and puree on high speed for 1 minute or until smooth and shiny. Using a rubber spatula, scrape down the sides of the bowl, then add the eggs. Process again until the mixture is smooth and shiny, about 2 minutes. Scrape the bowl again. With the machine running, slowly pour in the heavy cream. Scrape the bowl and process again to make sure the cream is completely incorporated. Remove the mixture and place in a bowl. Stir in the mustard, Worcestershire, and Tabasco, then gently fold in the cooled scallions and the crabmeat.
Place four or five 3- inch oiled ring molds into a lightly oiled nonstick pan. Fill each mold with the mixture, smoothing off the tops with a spoon. Over medium heat, cook the crab cakes until golden brown, about 2 minutes on each side. Once the cakes have browned, push down on the ring molds to cut off any excess crab mixture and remove the rings from around the cakes. Remove the crab cakes from the pan. Repeat the procedure until all of the crab mixture has been cooked. (The cakes may be made up to 1 day ahead, up to this point, and refrigerated.)
Preheat the oven to 400 degrees. Place the crab cakes on a buttered nonstick baking pan. Bake for 5 minutes or until the cakes are springy to the touch.
In a small pot, slowly heat the sauce over low heat without letting it boil. Place a small mound of the endive in the center of each serving plate. Top with 1 or 2 crab cakes then ladle the sauce over the crab cakes and serve immediately.