In a food processor combine the scallions and celery and process until finely chopped. Add the remaining patty ingredients, except the bread crumbs, and pulse briefly until the mixture forms a very chunky mixture, about 8 one-second pulses. There should be many pieces of shrimp remaining, each about the size of a pea. Transfer to a bowl. Add the panko to the shrimp mixture and stir gently until just combined. Form into four patties of equal size, each about 4½ inches in diameter and no more than ½ inch thick.
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Lightly coat a platter with oil. Arrange the patties on the platter, cover with plastic wrap, and refrigerate for at least 30 minutes or up to 2 hours.
Combine the sauce ingredients. Refrigerate until ready to use.
Prepare the grill for direct cooking over medium heat (350° to 450°F) and preheat a grill-proof griddle.
Prepare the grill for cooking over medium heat (400°F) and preheat a grill-proof griddle.
Lightly brush the patties on both sides with oil, place on the griddle, and cook over direct medium heat, with the lid closed, until golden and firm, about 8 minutes, carefully turning once after 5 minutes. During the last 30 seconds to 1 minute of grilling time, toast the buns on the cooking grates, cut side down, over direct heat. Build each burger on a bun with sauce, lettuce, a patty, onion, and pepperoncini, if using. Serve warm.
Lightly brush the patties on both sides with oil, place on the griddle, and cook over direct medium heat, with the lid closed, until golden and firm, about 8 minutes, carefully turning once after 5 minutes. During the last 30 seconds to 1 minute of grilling time, toast the buns on the cooking grates, cut side down, over medium heat. Build each burger on a bun with sauce, lettuce, a patty, onion, and pepperoncini, if using. Serve warm.
Lightly brush the patties on both sides with oil, place on the griddle, and cook over medium heat, with the lid closed, until golden and firm, about 8 minutes, carefully turning once after 5 minutes. During the last 30 seconds to 1 minute of grilling time, toast the buns on the cooking grates, cut side down, over medium heat. Build each burger on a bun with sauce, lettuce, a patty, onion, and pepperoncini, if using. Serve warm.
