Cook the fettuccine according to package directions until al dente.
While the pasta cooks, prepare the lobster tails by cutting them lengthwise.
Sauté garlic and shallots in olive oil until fragrant and translucent.
Add the lobster tails, cooking for 3-4 minutes until just opaque.
Stir in the cherry tomatoes and cook until they soften slightly.
Pour in the heavy cream and simmer for a few minutes until it thickens slightly.
Add Parmesan cheese and stir until melted and fully incorporated.
Combine the cooked fettuccine with the sauce, adding reserved pasta water as needed.
Finish with fresh basil, salt, and pepper to taste, then serve immediately.