Heat the butter in a large frying pan, add the shallots and cook over a low heat until softened. Stir in the tomato purée and cook for 1 minute. Meanwhile, remove the lobster meat from the shell and cut the tails in half. Add the lobster shell to the frying pan and cook for 5–10 minutes until browned.
Remove the pan from the heat and add the brandy. Return to the heat and boil vigorously until reduced down. Pour over the Madeira and bubble for 5–10 minutes until reduced by half. Pass through a sieve, pressing down hard to extract the juices.
Return the sauce to the pan. Mix together the cream, egg yolk and cayenne pepper. Add a tablespoon of the sauce to the cream mixture to warm a little, then stir the cream into the pan. Heat through but do not let it boil, then add the lobster meat.
Meanwhile, cook the pasta in a large saucepan of salted boiling water according to the pack instructions until al dente. Drain, reserving a little of the cooking water, and return to the pan. Toss the sauce through the pasta until coated all over, adding a little cooking water to loosen if needed, and season.
Spoon into serving bowls, top with the lobster tail and serve sprinkled with the tarragon.