Step 1Cut salmon into 1-inch pieces and place in bowl of food processor with mayonnaise, mustard, zest, shallot, tarragon, salt and pepper. Pulse to combine, stopping when you have small chunks that resemble a ground-meat mixture. Place in bowl and stir in bread crumbs. Divide mixture into 4 balls and compress tightly to form into patties.
Step 2Heat oil in large skillet over medium heat and cook burgers until lightly browned but cooked through, 3 to 4 minutes per side.
Step 3Use vegetable peeler to shave thin slices of fennel. Top burgers with fennel slices and serve open faced or sandwich-style on rolls spread with a few tablespoons of olive tapenade.