Lobster bisque—basically decadence in the form of soup—turns extra indulgent with cooked rice blended in as a thickener. Take the time to brown the butter to give it added nutty dimension, then garnish with halved claws for a show-stopping starter.
Prepare the lobster stock: Bring a large pot of salted water to a boil over high. Cook lobsters until bright red, about 8 minutes. Transfer lobsters to a bowl of ice water, and let stand 10 minutes. Remove lobster meat, reserving shells. Reserve 2 claws. Roughly chop tail meat, and cut remaining 4 claws in half lengthwise for serving; cover and chill.
Heat oil in a Dutch oven over medium. Add onion, celery, parsnip, and garlic; cook, stirring often, until softened, about 6 minutes. Add lobster shells, canned stock, and bay leaf. Bring to a boil over medium-high. Reduce heat to medium-low, cover, and simmer 45 minutes. Pour stock mixture through a fine wire-mesh strainer into a large bowl; discard solids. Reserve stock.
Prepare the bisque: Melt butter in a Dutch oven over medium. Cook, stirring often, until butter is nutty and golden brown. Add onion, parsnip, celery, and garlic; cook, stirring often, until softened, about 5 minutes. Add cayenne, and cook until fragrant, about 30 seconds. Add wine, and cook until almost dry, about 6 minutes. Add rice, and cook, stirring constantly, until lightly toasted, about 2 minutes.
Add reserved lobster stock to Dutch oven; bring to a boil over high. Reduce heat to medium-low, cover, and cook until rice is tender, about 20 minutes. Transfer stock-rice mixture and reserved 2 claws to a high-powered blender. Remove center piece of blender lid (to allow steam to escape); secure lid on blender, and place a clean towel over opening in lid. Process until smooth, about 45 seconds. Return soup to Dutch oven over low. Stir in heavy cream and salt until cream is heated through. Ladle into shallow bowls; top with chopped lobster meat, and sprinkle with chives. Garnish with halved lobster claws, if desired.