6 each 1 pound live Maine lobsters
As needed, salt
14 Tablespoons butter, softened
1 cup medium-dry or cream sherry
6 cups milk
2 cups heavy cream
1 pinch cayenne
1-2 pinches paprika
To taste, salt and freshly ground black pepper
½ teaspoon fresh lemon juice
2 springs parsley, leaves only, cut into thin strips
Plunge the Maine lobsters into a large pot of boiling salted water over high heat and boil until just cooked through, about 4 minutes. Transfer Maine lobsters to a large bowl of ice water to prevent them from cooking any longer, and keep them submerged until completely cool. Drain Maine lobsters; separate tails and claws from bodies, setting bodies aside. Crack shells and remove the meat from the tails and claws, reserving tail shells. Cut the Maine lobster meat into large pieces and set aside in the refrigerator.
Melt 8 Tablespoons of butter in a large, wide heavy-bottomed pot over medium-high heat. Add Maine lobster bodies and tail shells and cook, turning often, until shells turn deep red, 5-8 minutes. Add sherry and boil for 2 minutes, then add milk and cream and return to a boil. Reduce heat to medium-low and simmer, stirring often, until milk and cream reduce by one-quarter and thickens slightly, 20-25 minutes. Add cayenne, paprika, and season to taste with salt and pepper. Remove pot from heat, set this milk infusion aside to cool, cover, and refrigerate overnight. The following day, strain milk infusion into another medium pot, discarding solids, and bring just to a simmer over medium heat.
Meanwhile, melt 4 Tablespoons of butter in a large skillet over medium heat. Add Maine lobster meat and heat until warmed through, 3-5 minutes, and then add to milk infusion in pot. Add lemon juice and adjust seasonings. Divide stew between 6 warm bowls, add some of the remaining 2 Tablespoons butter to each bowl, and garnish with parsley.