Fill a large, deep pot with 14 cups of water. Bring water to a boil, place the lobster in the pot, and cook for 5 minutes. Once the lobster is cooked, chop the head and body off using a pair of scissors, cutting the shell on the back to the end. Remove the meat.
Slice the tail into 6 to 8 medallions. Crack the shell of the claws and separate the head shell from the body. Cut the body into 6 to 8 pieces, with each piece attached to a leg. Set aside for later.
Cut broccoli into small pieces. In a small pot, boil 3½ cups of water and add broccoli. Cook for 5 minutes. Drain and set aside for later use.
Using a mixing bowl, thoroughly mix egg whites and cream with salt and sugar.
Heat wok with cooking oil, pour in egg and cream mixture (from step 4), and lightly stir-fry over medium heat for 1 minute. Add lobster tail pieces and stir-fry for another minute.
Arrange the broccoli in a ring shape in the center of a round or oval shaped plate. Top with lobster and the egg/cream mixture (from step 5).
Surround broccoli with the cooked claws and body. Serve immediately.