Arrange an oven rack to 3 to 4 inches from the broiler element and heat the broiler. Line a rimmed baking sheet with aluminum foil.

Cut 1 pound skinless salmon fillets into 1-inch pieces. Halve 3 medium scallions, separating the green and white parts. Coarsely chop the scallion whites. Finely grate the zest of 1 medium lemon, then juice the lemon until you have 1 tablespoon.

Prepare the following, adding each to the bowl of a food processor as you complete it: If using, tear 2 slices white sandwich bread into 1-inch pieces; oick the leaves from 6 fresh parsley sprigs until you have ¼ cup; pulse until the bread is broken down into very small pieces, 4 to 5 (1-second) pulses. (If using panko breadcrumbs, add ⅔ cup to the food processor and skip pulsing.)

Add the salmon pieces and scallion whites, and pulse until coarsely ground, 10 to 15 (1-second) pulses.

Transfer salmon mixture to a large bowl. Add the lemon zest, 1 large egg, 1 ½ teaspoons Old Bay seasoning, ½ teaspoon kosher salt, and ¼ teaspoon black pepper. Gently fold together with a flexible spatula until combined.

Divide the salmon mixture into 4 portions (½ cup or 4 ½ ounces each). Form each one into a patty about 1 inch thick and 3 ½ inches wide. Place on the baking sheet.

Broil until the patties are lightly browned on top, 3 to 5 minutes. Flip the patties and continue to broil until they are just cooked through and register at least 125°F on an instant-read thermometer, 2 to 3 minutes more. Meanwhile, make the sauce.

Finely chop the scallion greens and place in a small bowl. Finely grate 1 garlic clove into the bowl. Add the lemon juice, ⅓ cup mayonnaise, and 1 pinch ground cayenne pepper. Stir until well-combined. Taste and season with more lemon juice, kosher salt, and black pepper as needed. Serve the patties topped with the sauce.