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1
Pulse bread in food processor to coarse crumbs, about 10 pulses. Transfer to bowl and set aside.
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2
Pulse shrimp in now-empty processor until some pieces are finely minced and others are coarsely chopped, about 7 pulses. Transfer shrimp to large bowl.
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3
Combine mayonnaise, scallions, parsley, lemon zest, cayenne, salt and pepper in large bowl until uniform, then gently fold into processed shrimp until just combined. Sprinkle bread crumbs over mixture and gently fold until incorporated.
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4
Scrape shrimp mixture onto small baking sheet, divide it into 4 equal portions, and loosely pack each into 1-inch-thick patty. Cover and refrigerate the patties for at least 30 minutes or up to 3 hours.
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5
To Grill: Clean and oil cooking grate. Lightly brush tops of patties with oil, lay them on grill, oiled side down and lightly brush other side with oil. Cook patties, without pressing on them, until lightly browned and cooked through, 10 to 14 minutes, flipping them halfway through grilling. Transfer burgers to platter, tent loosely with aluminum foil and let rest for 5 minutes before serving.
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6
Stovetop: Cook in a 12 inch nonstick skillet over medium-high heat using 1-2 teaspoons vegetable oil until shimmering. Gently lay the shrimp burgers in the skillet and cook until crisp and browned on both sides, 8 to 10 minutes.
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7
Sauce: Combine all ingredients together. Stir until well mixed.
