Bring a large pot of water to a boil and season generously with salt.
Using kitchen shears, split the lobster tails straight down the center through the shell. Remove the vein if present and rinse if needed.
2 lobster tails
Heat the olive oil in a wide, deep skillet over medium heat. Add the lobster tails and sauté until the shells turn bright red and the meat is just barely opaque, about 2 minutes per side. Remove the lobster tails to a plate and let cool. Once cool enough to handle, remove the meat from the shells and cut into bite-sized pieces. Reserve the shells.
3 tablespoons olive oil
Lower the heat to medium-low. Add the shallot and garlic along with a small pinch of salt. Cook until softened and fragrant with no color, about 3-4 minutes. Add the red chili flakes and cook for about 30 seconds.
1 shallot, 4 cloves garlic, kosher salt, 1-2 teaspoons red chili flakes
Stir in the tomato paste and cook, stirring constantly, until it darkens slightly and caramelizes, about 2 minutes.
2 tablespoons tomato paste
Carefully add the brandy and cook until completely evaporated, scraping up any browned bits, about 1 minute. Add the white wine, reserved lobster shells and bay leaf, then simmer until reduced by about half, 2-3 minutes.
2 tablespoons brandy, ½ cup dry white wine, 1 bay leaf
Add the crushed tomatoes and clam juice. Bring to a gentle simmer, then lower the heat and cook uncovered for about 20 minutes so the sauce concentrates and pulls flavor from the shells.
1 28-oz can tomatoes, 1 cup clam juice
While the sauce simmers, cook the linguine until just shy of al dente. Reserve at least 1 cup of pasta water, then drain.
½ lb linguine
Remove and discard the lobster shells and bay leaf from the sauce. Add the pasta directly to the pan and toss to coat, loosening with pasta water as needed until the sauce clings nicely to the noodles.
Turn the heat to the lowest setting, then add the butter and toss until melted and glossy.
3 tablespoons butter
Stir in the sherry and the reserved lobster meat and cook gently until just cooked through, about 1-2 minutes.
2 tablespoons sherry
Taste and adjust seasoning with salt as needed.
Finish with the parsley right before serving. Divide the pasta between two bowls and serve immediately.
1 tablespoon flat leaf parsley