For the Herbed Sherry Mayo:
2 cups mayonnaise (Hellmann’s or Best Foods)
3 tablespoons tarragon vinegar, white wine vinegar, or rice vinegar
3 tablespoons dry sherry
2 teaspoons sugar
2 teaspoons finely chopped fresh herbs (equal parts chives, parsley, tarragon, and basil, or whatever you have)
For the patties:
1 scallion, finely chopped
1 finely chopped fresh basil
1 all-purpose flour, for dusting
12 ounce salmon fillet
1/2 cup olive oil, plus more if needed
1 red onion, finely chopped (about 1 cup)
1 teaspoon Tabasco sauce
1 1/2 cups plain dried bread crumbs
1 large egg
1 teaspoon kosher salt
Freshly ground black pepper
4 hamburger buns, split and toasted
4 lettuce leaves
4 tomato slices
4 thin slices red onion
For the mayo: Whisk together all the ingredients for Herbed Sherry Mayo in a large bowl. (The mayo will keep in your fridge for up to 1 week, tightly covered.)
For the burgers: Cut the salmon fillet into 3 or 4 pieces and pulse in a food processor about 10 times, until coarsely ground. Don't overmix; you don't want the fish to turn into paste. Add the onion, bread crumbs, egg, and Tabasco and pulse a few times.
Transfer to a large bowl. Mix in the scallion, basil, salt, and 1/4 teaspoon pepper.
Shape the mixture into 4 patties, sprinkling on a few drops of water if the mixture is too dry to hold together. Pour the flour onto a plate and add a few grinds of black pepper. Lightly coat the salmon patties with flour on each side and set them on a pl
Pour the oil into a large skillet (it should be 1/4-inch deep) and heat over medium-high heat until the oil shimmers but is not yet smoking. Gently place the salmon patties in the hot oil and cook until golden brown, about 3 minutes on each side.
Line a plate with paper towels. When the burgers are done, transfer them to the paper-lined plate.
To assemble the burgers: Place each salmon burger on the bottom of a bun, spoon on the mayo, and top with the lettuce, tomato, and onion. Cover with the top half of the roll and serve.
Cat's Note: To make this an appetizer, shape the salmon mixture into 15 small cakes, 1 1/2 inches across, and cook the mini salmon cakes for about 1 1/2 minutes on each side. Serve with a dab of mayo or spoon the mayo into ramekins for dipping.