The foregoing is excerpted from Union Square Cafe Cookbook by Danny Meyer and Michael Romano. All rights reserved. No part of this book may be used or reproduced without written permission from HarperCollins Publishers, 10 East 53rd Street, New York, NY 10022
Make the glaze: Combine all the glaze ingredients in a 1-quart saucepan and bring to a boil. Lower the heat and simmer until the glaze coats the back of a spoon, about 5 minutes. Strain through a sieve and reserve in a warm place until tuna burgers are cooked. (The glaze can be prepared up to 2 days ahead and stored, covered, in the refrigerator.)
Make the burgers: Grind the tuna in a meat grinder or chop with a large sharp knife to the texture of hamburger meat. (Do not use a food processor, which will shred the tuna rather than chop it.)
Transfer the ground tuna to a bowl and combine with the garlic, mustard, cayenne, salt, and pepper. Mix thoroughly. Divide the tuna into 4 equal portions. Using your hands, roll each part into a smooth ball and then flatten into a compact patty.
Heat the olive oil in a large skillet over medium-high heat and sear the tuna burgers until browned and medium rare, 3 to 4 minutes a side. Serve each burger on a buttered toasted bun and spread with a tablespoon of warm glaze. Garnish the burgers with equal amounts of pickled ginger slices.