Bring a large pot of water to a boil. Drop live lobsters into water head first and cover for 8 minutes. Remove lid; carefully remove lobsters and place in ice water to cool.

Twisting over a bowl to catch the juices, separate lobster head, tail, claws and knuckles; place extremities aside. Repeat with second lobster.

Cut meat from lobster heads into quarters with a heavy knife keeping all juices together in a bowl (this will add flavour to the sauce).

In a large pot over medium heat, add 2 tbsp (30 mL) of olive oil, shells of lobster heads, carrot, celery, onion and tarragon stems. Cook for approximately 5 minutes until vegetables just begin to cook. Add white wine and cook for 3 more minutes. Add tomatoes, 2 pinches of salt and lobster juice from bowl.

Pour hot water into pot, just covering lobster shells. Reduce heat to medium low and cook for 45 minutes.

While sauce is simmering, crack lobster claws and knuckles using a pair of sturdy kitchen shears with a cracker. Pick out meat and remove cartilage fin from centre. Using shears, cut tail shell lengthwise and remove meat. Cut tail meat into 1 inch pieces, set aside with claw meat.

Bring a large pot of salted water to a boil.

Strain sauce, reserving all of the liquid. Pour liquid back into pot and reduce to approximately 2 cups. It should have a prominent, bright, herbaceous and briny lobster flavour.

Add spaghetti to boiling water and cook according to package directions.

In a large straight sided sauté pan over medium heat, combine lobster sauce, lobster meat, spinach, all herbs, lemon juice, lemon zest and butter. Stir gently. Adjust seasoning with a few pinches of salt, ground pepper and chili flakes, if desired.

Add strained pasta to sauce and gently mix together, coating all noodles with sauce. Divide pasta into bowls; garnish with extra herbs. Spoon extra sauce and drizzle olive oil over each dish.