Finely mince the 3 garlic cloves and thinly slice the 2 shallots. Halve the cherry tomatoes lengthwise, strip the tarragon leaves from their stems, zest the lemon, and snip the chives into small pieces. Bring a large pot of salted water to a boil and add the 8 oz pasta, cooking until al dente according to package directions (usually 9-11 minutes). Reserve 1 cup of pasta water before draining, then set the cooked pasta aside.
While the pasta cooks, cut the 2 lobster tails into 1-inch bite-sized chunks and set aside. Heat 2 tbsp olive oil in a large pan over medium heat, then add the sliced shallots and minced garlic. Sauté for 2-3 minutes until fragrant and softened, stirring occasionally. Add the cherry tomatoes and cook for another 2 minutes until they begin to soften.
Pour in the 1/4 cup white wine and stir, scraping up any flavorful bits from the bottom of the pan. Let it simmer for 1-2 minutes to reduce slightly and burn off the alcohol. Reduce heat to medium-low, then add the lobster chunks, tarragon leaves from Step 1, and 3/4 cup cream to the pan. Simmer gently for 3-4 minutes, stirring occasionally, until the lobster is just cooked through and the sauce has slightly thickened.
Remove the pan from heat and stir in 3 tbsp butter and the lemon zest from Step 1 until fully incorporated and the sauce becomes silky. Add 1 tsp lemon juice for brightness. Taste and season with salt, pepper, and a pinch of ground nutmeg—I like the nutmeg to add a subtle warmth that complements the richness of the lobster without being obvious.
Add the cooked pasta from Step 1 to the lobster cream sauce and gently toss to combine. If the sauce seems too thick, add a splash of the reserved pasta water (1-2 tbsp at a time) until it reaches a silky consistency that coats each strand. Divide among serving bowls and top each portion with fresh chives, a pinch of red pepper flakes for heat, and a generous shaving of parmesan cheese.