Cut fish into 1-inch pieces. Place one-third of the fish and 1/3 cup of the whipping cream in blender container. Cover and blend on high speed, stopping blender occasionally to scrape sides if necessary, until smooth and thick, about 1 minute.
Pour mixture into large owl. Repeat twice with remaining fish and 2/3 cup of the whipping cream. Shake remaining 1/2 cup whipping cream and the cornstarch in tightly covered jar. Stir cornstarch mixture, salt and red pepper into fish mixture. Beat vigorously with spoon until well blended and fluffy.
Spread fish mixture in an oiled loaf pan or 6-cup mold; cover with aluminum foil. Place pan in a 13 x 9-inch pan on oven rack. Pour hot water into pan until almost full. Bake at 350 degrees F until knife inserted in center comes out clean, 60 to 70 minutes.
While the pudding bakes, make the sauce.
Cook and stir mushrooms in butter in 2-quart saucepan over medium heat 3 minutes; remove from heat.
Stir in flour, salt and pepper. Gradually stir in half-and-half. Heat to boiling over medium heat, stirring constantly. Boil and stir 1 minute. Remove from heat; stir in dill weed.