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1
Bring 6 quarts water with 3 tablespoons salt to a boil in an 8- to 10-quart pot over high heat.
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2
Meanwhile, stir together cornstarch, broth, rice wine, soy sauce, sugar, and pepper in a small bowl until sugar is dissolved.
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3
Plunge lobsters headfirst into boiling water, then cover tightly and cook for 2 minutes from time lobsters enter water. Transfer lobsters with tongs to a large bowl of ice and cold water to stop cooking (lobsters will not be fully cooked), then drain lobsters in a colander. When cool enough to handle, twist off tail and claws (including joints) of 1 lobster. Cut body in half lengthwise through shell with shears, then remove and discard sand sacs from inside head. Cut body in half again crosswise. Halve tail lengthwise through shell with a cleaver or large heavy knife, then cut each half crosswise into 4 pieces. Working with same lobster, 1 claw at a time, wrap claws with joints in a kitchen towel and twist off claws from joints. Unwrap claws, then crack joints with a mallet or back of a large heavy knife. Chop claws in half lengthwise between pincers with a cleaver or large heavy knife. Transfer lobster pieces to a bowl, keeping meat in shells. Repeat with second lobster, putting pieces of second lobster in another bowl.
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4
Heat wok over high heat until a drop of water evaporates instantly. Pour 1 tablespoon vegetable oil down side of wok, then tilt wok to swirl oil, coating side. When oil begins to smoke, add pieces of 1 lobster and stir-fry just until meat starts to turn opaque, about 1 1/2 minutes. Transfer cooked lobster with a slotted spoon to a large bowl. Repeat with second lobster, transferring cooked pieces to same bowl.
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5
Add remaining tablespoon vegetable oil to wok, swirling to coat, then add beans, garlic, ginger, scallions, and pork and stir-fry until pork is no longer pink, about 1 minute.
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6
Stir cornstarch mixture, then add to pork in wok and bring to a boil. Add lobster and stir to coat, then reduce heat and simmer, covered, 2 minutes. Remove lid and pour eggs over lobster mixture in a thin circular stream. Cover wok and simmer just until eggs begin to set, 1 to 2 minutes. Drizzle with sesame oil, then gently toss. Serve immediately.
