Fill a large pot with 2 inches of water; bring to a boil. Add the lobsters, cover and cook over medium heat until the shells turn bright red, 8 to 10 minutes. Remove with tongs and rinse under cold water to cool slightly. Meanwhile, cut the kernels off the corn; reserve the cobs.
Remove the meat from the lobster shells: Twist off the claws, then break off the tail; set the bodies aside. Pull the flippers off the tail, then insert your thumb into the flipper end and force out the meat. Crack the claws with a lobster cracker, mallet or the flat side of a knife and remove the meat. Chop the lobster meat into 1-inch pieces and transfer to a bowl; cover and refrigerate until ready to use.
Rinse the lobster bodies to remove any green matter (tomalley) and roe. Heat 2 tablespoons butter and the olive oil in a large saucepan over medium-high heat. Add the lobster bodies and cook, turning occasionally, until the butter starts to brown, about 3 minutes. Add the wine, bring to a boil and cook until reduced by half, about 2 minutes. Add the corn cobs, celery stalk, whole shallot, parsley sprigs and 6 cups water; bring to a boil, then lower the heat and simmer until the liquid is reduced by about one-third, about 30 minutes. Strain the stock into a bowl or large measuring cup.
Heat the remaining 1 tablespoon butter in a saucepan over medium heat. Add the diced shallot and cook until softened, about 2 minutes. Add the tomato paste and paprika; cook, stirring, until slightly darkened, about 1 minute. Stir in the prepared stock and cream and simmer until reduced by one-third, about 20 minutes (you should have 2 3/4 cups sauce). Add the corn kernels; simmer 5 more minutes.
Bring a large pot of salted water to a boil. Add the pappardelle and cook as the label directs. Drain, then return to the pot. Add the sauce and the reserved lobster meat and cook over medium heat, stirring, until the lobster meat is heated through, about 1 minute. Stir in the chopped celery leaves and parsley and most of the chervil. Divide among plates and top with the remaining chervil.