Make sure meat is dethawed before cooking.
Remove meat from lobster tails and chop into 1-inch chunks (each tail typically yields 8 pieces).
Bring a large pot of salted water to a boil.
Add pasta and cook according to package directions.
Heat olive oil in a large saucepan over medium-high heat.
Add the shallots, sautéing until soft.
Add the garlic and cook for 1 minute, until fragrant. Be careful not to cook on too high of heat so you don’t burn the garlic.
Add the cherry tomatoes and sauté until they burst and release their juices.
Add the Champagne and simmer until about half the liquid is remaining (feel free to add an extra splash of Champagne). Add the heavy cream and heat through.
Add the Parmesan cheese and stir until melted.
Add the black pepper and lemon zest.
Then, add the raw lobster tail pieces and heat through until lobster is fully cooked.
Add in the cooked pasta and mix.
Add reserved pasta water to pan if pasta is too dry.
Plate in individual bowls and top with tarragon leaves.