Put the hard-cooked egg in a small sieve and using the fingers, press it through. Scrape off the sieved part that clings to the sieve into the mayonnaise.
Add the anchovy paste, pickles, capers, parsley, chives, and tarragon. If desired, add salt and pepper, a little at a time. Stir in a little lemon juice and mix. Serve with cold shellfish such as shrimp, lobster, or crab meat or with cold poached fish.