Cook pasta according to package directions, drain.
While pasta cooks, bring the wine, chicken stock, and a thyme sprig to a boil in a large skillet. Add the lobster tails. Cover, reduce heat, and simmer 5 minutes or until done. Remove the lobster from pan, and cool slightly. Remove the meat from the lobster tails; coarsely chop.
(In a separate pan, sauté your sliced mushrooms with olive oil and a little salt.)
Back to the pan with the wine mixture, add the olive oil, salt, and pepper to the wine mixture in pan; bring to a boil. Cook 14 minutes or until reduced to 1/2 cup. Discard the thyme sprig. Stir in the cream. Add lobster meat, mushrooms and pasta to sauce. Cook 1-2 minutes or until the sauce coats the pasta, and toss. Sprinkle with parsley, thyme and some Parmigiano-Reggiano if desired. Serve immediately.