Warm 1 tablespoon seafood stock, add the saffron threads, and set aside to bloom.

Bring a pot of well-salted water to a gentle boil. Add the lobster tails and cook 4–5 minutes, until the shells are bright red and the meat is just opaque. Transfer briefly to ice water, remove the meat from the shells, and slice each tail in half lengthwise for plating. Reserve the lobster cooking water for the pasta.

In a large skillet, cook the butter over medium heat until nutty and lightly browned. Add the panko and a pinch of salt and toast until deeply golden. Remove from the heat, stir in the lemon zest and chives, then transfer to a bowl. Wipe out the skillet.

In the same skillet, melt 3 tablespoons butter, letting it lightly brown if you want extra depth. Add the shallot and cook 2–3 minutes until soft, then add the garlic and cook for 30 seconds. Stir in the tomato paste and cook, stirring constantly, 3–4 minutes until brick-red and sweet-smelling. Deglaze with the cognac and simmer until reduced by about half and the sharp alcohol smell is gone. Add the seafood stock, saffron bloom (threads and liquid), heavy cream, bay leaf, and tarragon sprig. Simmer 18–20 minutes, stirring occasionally, until thick, glossy, and bisque-like. Remove the bay leaf and tarragon and season lightly with salt and pepper.

Stir the cooked lobster meat into the sauce and warm gently for 1–2 minutes, keeping the heat low.

Bring the reserved lobster cooking water back to a boil. Cook the spaghetti until just shy of al dente, reserving at least 1½ cups pasta water. Transfer the spaghetti directly into the sauce and toss, adding ¾–1 cup pasta water until the sauce is loose, silky, and generously coats the pasta. Finish with the cold butter.

Twirl the pasta into bowls, spoon extra sauce over the top, add a lobster tail half (and a claw, if using), and finish with the brown butter chive crunch.