Begin by breaking down the lobster. If you're breaking down a whole, live lobster, begin by taking a sharp knife and cutting down–hard–on the line at the top of the head (I know, its gruesome). This kills the lobster immediately and prevents any further suffering. From there, twist off the tail, then the claws, and proceed to remove the shell using a pair of scissors. Alternatively, after killing the lobster, boil it whole until cooked through.
If using lobster tails from the grocery store or fish market, just take kitchen shears and cut down the middle of the shell from top to the end of the tail. Do this on the top and bottom sides of the lobster tail. Then, gently pull the lobster tail meat out. Give the meat a rough chop.
Mince the garlic and shallot, along with the fresh tarragon. Zest the lemon and slice the cherry tomatoes in half lengthwise.
Bring a large pot of salted water to a boil and cook pasta according to package instructions until al dente. Drain and reserve a cup of pasta water just in case.
In a large skillet over medium heat, add about 2 tablespoons of olive oil and the mince shallots. Sweat until translucent, then add the minced garlic. Once softened, add the cherry tomatoes and toss until they begin to blister. Then, add the white wine (off of the flame, but while pan is still hot) and use a wooden spoon to scrape any bits off of the pan.
Add in the uncooked lobster meat, the minced tarragon, and the heavy cream. Sauté lobster meat until cooked through.
If you are using boxed pasta, rather than fresh, reduce the amount of cream by HALF, adding more as needed.
Add butter and emulsify, along with lemon zest. Simmer on low.
Add the cooked pasta to the sauce and toss to combine. Season with salt and pepper and, if necessary, add any more pasta water or cream until the sauce is the consistency you like.
Garnish with more lemon zest or lemon juice, fresh chopped chives, and red pepper flakes. Parmesan cheese is optional on top.