in a small bowl, combine the hoisin sauce and soy sauce with 1/3 cup water.
In a large skillet or wok, heat 1 tbsp. oil over medium-high. Add the chicken and cook, breaking apart with a wooden spoon, until browned, 4 minutes.
Reduce the heat to medium, add the carrot and the remaining 1 tbsp. oil and cook, stirring, 2 minutes. Add the garlic and scallion whites and cook 1 minute. Stir in the hoisin mixture and cook until the sauce thickens and coats the chicken and vegetables, 1 to 2 minutes.
Divide the lettuce leaves among 4 plates. Top each leaf with the chicken mixture; sprinkle with the scallion greens.