Begin by breaking down the lobster tails. Use kitchen shears to cut down the "spine" of the tail, with the scissor blade between the lobster meat and the shell. Do this on the top and bottom sides of the tail. Then, carefully, pull the lobster meat out of the shell. Set the shells aside.
Use a sharp knife to cut the uncooked lobster tail meat into roughly ½-inch pieces.
Finely dice the shallot and mince the garlic cloves. Zest the lemons, then squeeze the juice from them.
Remove the tarragon leaves from the stem, roll the leaves up, and give it a rough chop.
In a large pan with high sides (a saucier or sauteuse is great here), add a small amount of olive oil (about 1 tablespoon or less) along with 1 tablespoon of butter and allow to melt over medium-high heat.
Add in the diced shallot and garlic, allowing to sweat and become translucent, making sure they do not burn.
Add in the lobster shells. Stir and sauté until the shells turn a bright red color from the heat, about 5-7 minutes. Once shells are red, move them to the side and add the tomato paste directly to the pan. Cook the tomato paste while stirring for 2 minutes.
Add the brandy to the hot pan (but remove from a flame first), then add the white wine. Use a spatula or wooden spoon to scrape the bottom of the pan for any bits of food. Allow the alcohol to reduce by simmering until the pan is nearly dry. Add the heavy cream and simmer until thickened, about 5 minutes.
Place a pot in the sink with a fine-mesh strainer or sieve over the top of it. Remove shells, then pour the contents of the lobster sauce into the sieve, and gently press to make sure all of the sauce ends up in the pot.
Place pot back on the stove over low heat. Add lemon juice, salt & pepper, parmesan cheese, and the diced lobster meat. Stir over low heat until the meat is cooked through.
Add 1-2 tablespoons of cold butter, along with the fresh tarragon, and stir until the butter is emulsified in the sauce.
Cook ravioli according the package directions and reserve a small amount of pasta water if needed.
Add the cooked ravioli to the lobster sauce pot, and stir to combine. If necessary, add a small amount of pasta water to loosen the sauce. Taste and add more salt and pepper as needed.
Serve hot in a bowl and garnish with lemon zest, any remaining chopped tarragon, and fresh chopped chives. Add red pepper flakes if desired. Enjoy.