Boil a large pot of salted water. Place the lobsters into the boiling water, and cook for 5 minutes. Remove the lobsters from the boiling water and quickly transfer them to a large bowl filled with ice water to cool.
When the lobsters are cool enough to handle, remove the tail and claw meat, and coarsely chop. Hold on to the shells. Tightly cover the meat and refrigerate.
In a large Dutch oven, melt a stick of butter over medium-high heat. Add the shells and cook, stirring, until they turn bright red (usually in 2 to 3 minutes). Add 1/2 cup of the sherry and bring the mixture to a boil. Cook until reduced by half (usually about 3 minutes).
Add the milk, cream, cayenne, paprika, salt and pepper, and return to a boil. Once the mixture has reached a boil, reduce the heat to medium-low and simmer until it is slightly thickened (usually15 to 20 minutes). Remove from the heat and let it cool. Cover and refrigerate at least 6 hours or overnight for the flavors to fully develop.
Remove the milk and shell mixture from the refrigerator and strain it into a container through a fine mesh strainer, setting aside the portion caught in the strainer.
In a large pot, melt the remaining stick of butter over medium-high heat. Add the chopped lobster meat and cook, stirring, until the meat is lightly colored (usually 2 to 3 minutes).
Add the remaining 1/4 cup of sherry and turn the heat up to high. Cook while stirring, to deglaze the pan, until the mixture is reduced by half. Add the strained milk mixture and bring to a low boil. Simmer and stir until the stew is heated through.
Remove the stew from the heat and season to taste. Spoon into bowls and garnish with chopped fresh parsley. Serve immediately.