In a Dutch oven, add the salt to 1" of water and bring to a boil. Add the lobsters and cook for 8 mins until the lobsters are slightly undercooked. Transfer the lobsters to a baking sheet and let sit until cool enough to handle.

Remove all the meat from the lobsters, chill and set aside. Remove tomalley (green matter) from meat (and reserve if the lobsters are not from the region with red tides recently).

Add the shells back to the pot with onion, parsley and garlic. Bring to a boil, then reduce to a simmer and cook for 45 mins.

Skim any foam that rises to the top. Strain the stock and put it back to the same pot.

Add cream to the stock (and thre tomalley). Mix to combine. Lower heat to a simmer and allow sauce to reduce, cook for about 5 minutes.

Add the cherry tomatoes and paprika. Add flour for thicker sauce, if necessary.

Meanwhile, in a separate pot, melt butter on low heat. Add the lobster meat and season with salt and peper. Transfer the lobster meat to a serving platter. Set aside.

In the same pot, cook the pasta until it has 4 mins left to cook. Add the pasta to the sauce. Toss over medium-high heat until the paste is coated with sauce and al dente.

Add the lobster meat to the pasta and mix to combine. Taste and adjust the seasoning, if necessary.

Transfer to a serving platter. Garnish with the chopped parsley. Serve immediately.