If your lobster tails are 4-5 ounces, cook the lobster in boiling water for about 4-6 minutes. There are a lot of videos available on youtube on how to properly remove the lobster shell. Cut the lobster meat into chunks or you can finely chop it so that it is evenly distributed throughout the sauce.
In large pan, sauté the onions with 3 tablespoons of unsalted butter. Then add the garlic, chopped celery and cook for about 1 minute on medium heat - stirring constantly.
Add the chopped tarragon, red crushed pepper, salt, black pepper and stir.
Add the cream and bring it to a boil.
Lower the heat and allow the sauce to simmer for 15 minutes.
Two options: (1) you can allow the sauce to cool after 15 minutes and place it in a blender and pour back in the pan to continue simmering for another 5-10 minutes or (2) allow the sauce to simmer for another 10-15 minutes to allow the spices and celery, garlic and onion to infuse the cream and then pour through a sieve to remove everything.
What I did was blend the sauce with everything and then poured it through a sieve at the end for a creamier sauce.
After pouring through a sieve, pour the sauce back in the pan and add a couple of slices of lobster meat and on low heat allow the lobster to flavor the sauce for a couple of minutes.
Cook the pasta according to the packaging instructions. Make sure to reserve about a 1/2 cup of pasta water.
Turn the heat off and add 1/4 cup of freshly grated parmesan cheese, lobster meat, lemon zest, lemon juice and additional salt if it needs it.
Add the pasta and stir.
Add a little bit up pasta water , 1 tablespoon of butter and stir to loosen the sauce and pasta. Add as much of the pasta water you need - to reach your desired sauciness.
Top the pasta with freshly ground black pepper, parmesan and chives. Enjoy!
