Have a live lobster steamed at the grocery store about an hour before you plan on making this dish. If you're brave you can steam your own live lobster, but avoid purchasing raw lobster meat and then bringing it home to cook, as it spoils quickly and your dish won't taste as fresh, or you may get food poisoning!
Break into your lobster and chop the meat.
Begin bringing your pasta water with salt up to a boil.
Melt 1 Tbsp of butter over medium-low heat. Once the pan is hot, add minced shallots and a pinch of saffron that you have rubbed between your fingers. Sauté until the shallots begin to soften and the saffron becomes aromatic.
Turn the pan up to medium heat and add the flour into the pan, stirring it into the butter. Cook for 1 minute. Add the wine and cook for 1 minute while rubbing a wooden spoon along the bottom of the pan.
Add the clam juice and tomato paste to the pan. Continue to stir frequently with a wooden spoon and bring up to a simmer. Once simmering, decrease the heat to low and cook at a low simmer for 10 minutes, while stirring on occasion.
While the sauce is simmering, add your linguine to the boiling water and cook according to package instructions using the lower recommended cooking time so that it is al dente.
Add the whole milk and heavy cream to the pan and stir it into the sauce until smooth. Heat through, but don't allow the sauce to bubble. Remove from the heat.
Add the linguine from the pot of boiling water into the pan with the sauce. Be sure to reserve the pasta water and add it to the dish as needed if the pasta appears dry. Fold in the fresh lobster meat. Season with salt and pepper to taste. Garnish with fresh parmesan and parsley as desired. Serve immediately.