Bring a large pot of salted water to a boil. Plunge the lobsters head first into the boiling water, in batches, if necessary, and cook, covered, for 5 minutes. Transfer the lobsters with tongs to a large bowl filled with ice water to cool. When the lobsters are cool enough to handle, crack the shells, remove the tail and claw meat, and coarsely chop. Reserve the shells. Tightly cover the meat and refrigerate.

In a large Dutch oven, melt 4 ounces (1 stick) of butter over medium-high heat. Add the shells and cook, stirring, until they turn bright red, 2 to 3 minutes. Add 1 cup of the Sherry and bring to a boil. Cook until reduced by half, about 3 minutes. Add the milk, cream, paprika, salt, and pepper, and return to the boil. Reduce the heat to medium-low and simmer until slightly thickened, 15 to 20 minutes. Remove from the heat and let cool. Cover and refrigerate at least 6 hours or overnight for the flavors to develop.

Remove the milk and shell mixture from the refrigerator and strain into a clean container through a fine mesh strainer. Set aside. In a large, heavy pot, melt the remaining 4 ounces (1 stick) of butter over medium-high heat. Add the chopped lobster meat and cook, stirring, until lightly colored, 2 to 3 minutes. Add the remaining 1/2 cup of Sherry and increase the heat to high. Cook, stirring, to deglaze the pan and until reduced by half. Add the strained milk mixture and bring to a low boil. Simmer, stirring, until heated through.

Remove from the heat and adjust the seasoning, to taste. Spoon into bowls and garnish with chopped fresh parsley. Serve immediately.