Cook the pasta in a large pot of boiling water per directions and drain, reserving ½ cup of pasta water.
Meanwhile, heat the olive oil in a large, heavy skillet over medium-high heat. Add the onion and cook for about 4 minutes.
Then add the garlic, red pepper, flakes, salt, pepper, and oregano. Stir together and cook for about 1 minute.
Add the cognac and scrape up any brown bits. Add the tomatoes, lobster, parsley and chopped basil. Cook, stirring, until is is heated through.
Add the linguine to the pot and stir to combine it with the sauce. If the sauce is too dry, stir in a little of the reserved pasta sauce. Serve and top each serving with a lobster claw (if you have it) and a basil sprig.