In a large bowl, beat egg to blend. Add crab, shrimp, rockfish, bread crumbs, green onions, bell pepper, broth, and mustard. Gently shape mixture into 8 equal patties about 3 inches wide and 3/4 inch thick; set slightly apart on a sheet of waxed paper or foil.
Pour 1/2 tablespoon oil into a 10- to 12-inch nonstick frying pan over medium-high heat. When hot, add half the crab cakes and cook, turning once, until cakes are browned on both sides and seafood in center of thickest part is opaque but still moist-looking (cut to test), 6 to 8 minutes total. As cakes are cooked, transfer to an ovenproof platter and keep warm in a 200° oven. Add remaining 1/2 tablespoon oil to pan and cook remaining cakes.
Serve crab cakes with mandarin chutney and salt and pepper to add to taste.
How to cook crab
Keep live crabs loosely covered in the refrigerator up to 12 hours. Grasp crabs carefully from the rear end, between the legs, and put in a pan to make sure they fit, with 3 to 4 inches of clearance below pan rim. Remove crabs and fill pan with enough water to cover crabs by 2 to 3 inches. Cover pan and bring water to a boil over high heat.
One at a time, grasp crabs as described above and plunge them headfirst into the boiling water; if you have too much water, ladle out excess and discard. Cover pan and start timing. When water resumes boiling, reduce heat to a simmer. Cook 1 1/2- to 2 1/2-pound crabs 15 minutes, 3-pound crabs about 20 minutes.
Drain crabs; to be able to handle quickly, rinse briefly with cool water.
How to clean, crack, and shell crab
Pull off and discard triangular flap from belly side.
Turn crab belly side down; pulling from the rear end, lift off back shell. Drain and discard liquid from shell. If desired, scoop soft, golden crab butter and white crab fat from shell into a small bowl to eat by the spoonful with crab or to stir into a dipping sauce. If using back shell for garnish, break bony section (mouth) from front end of shell and discard. Rinse shell well and drain.
On the body section, pull off and discard reddish membrane that covers the center (if it hasn't come off with the back) and any loose pieces. Scoop out any remaining golden butter and add to bowl. Pull off and discard long, spongy gills from sides of body. Rinse body well with cool water.
Twist legs and claws from body. Using a nutcracker or wood mallet, crack the shell of each leg and claw section. With a knife, cut the body into quarters.
Break apart legs and claws; using your fingers, a small fork, a pick, or a crab leg tip, remove meat. Pull body sections apart and dig out pockets of meat. Discard shells. One cooked, cleaned 1 3/4- to 2-pound crab (with back shell) yields 7 1/2 to 8 ounces (1 1/3 to 1 1/2 cups) of meat; heavier crabs do not always have more meat.