Begin by poaching the lobster tails. Add the wine and thyme to a medium saucepan. Bring to a boil. Once boiling, add lobster tails and reduce heat to medium. Cover and simmer for 5-6 minutes, or until they turn red and curl up into almost a ball. Remove from saucepan and let cool. Using kitchen shears or scissors, carefully cut down the belly of the lobster tail to remove the meat and chop into chunks. Set aside.

Bring a large pot of water to a boil for the pasta, and season with a couple big pinches of salt. Cook pasta until al dente. (Don't forget to scoop out your pasta water before you drain it! I like to keep a mug or heat-safe measuring cup next to the stove so that I don't forget.)

Meanwhile, start the cream sauce. Heat the olive oil in a large, nonstick skillet over medium heat. Add the shallot and garlic and season with a pinch of salt and a few turns of freshly cracked black pepper. Sauté for 1-2 minutes, stirring frequently, until fragrant and until you're just starting to see some caramelization. Add the cream, raise heat slightly and bring to a slow simmer. (Be sure to not heat the cream too high or bring it to a boil, or else the cream can separate!)

Once cream is just bubbling, reduce heat and add the butter, lemon zest, parmesan, and salt. Stir until butter and parm are melted, and mixture is smooth and creamy. Start by adding 1/4 cup of the reserved pasta water and lemon juice and stir to combine. Add the chopped lobster into the sauce to heat through, for about 1 minute, stirring constantly. Season to taste with additional salt and pepper, if needed. Add the pasta and toss with tongs until the sauce coats the pasta. If the sauce seems like it's too thick and needs a little loosening up, add another splash of pasta water until the sauce coats the pasta to your liking.

Portion into bowls and garnish with fresh basil leaves, lemon zest, freshly cracked black pepper, and lemon wedges. Serve immediately.