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Rinse whole lettuce leaves and pat dry, being careful not tear them. Set aside.
Heat a large skillet over medium-high heat. Cook and stir beef and cooking oil in the hot skillet until browned and crumbly, 5 to 7 minutes. Drain and discard grease; transfer beef to a bowl. Cook and stir onion in the same skillet used for beef until slightly tender, 5 to 10 minutes. Stir hoisin sauce, garlic, soy sauce, vinegar, ginger, and chile pepper sauce into onions. Add water chestnuts, green onions, sesame oil, and cooked beef; cook and stir until the onions just begin to wilt, about 2 minutes.
Arrange lettuce leaves around the outer edge of a large serving platter and pile meat mixture in the center.