Heat a teaspoon of vegetable oil in a large skillet over medium-high heat until shimmering, and then add the minced garlic and ginger. Sauté for about 30 seconds until fragrant, with a warm spicy aroma filling the air.
Add the ground chicken to the skillet, breaking it apart with a spatula. Cook for 5-7 minutes, stirring frequently, until the chicken is browned and cooked through, with a glossy, slightly caramelized surface.
Stir in the fish sauce and hoisin sauce, mixing well so the meat absorbs the savory flavors. Cook for another 2 minutes until the mixture is glossy and fragrant, filling the air with a rich aroma.
Remove the skillet from heat and fold in the sliced scallions and julienned carrots, adding freshness and crunch to the savory filling. Taste and adjust seasoning if needed.
Prepare a serving platter with the washed and dried lettuce leaves, arranged neatly for easy assembly.
Spoon a generous amount of the cooked chicken mixture into the center of each lettuce leaf. Gently wrap or fold the leaf around the filling, pressing softly to contain everything inside.
Drizzle a few drops of sesame oil over the assembled wraps, and serve immediately for the best crunch and flavor. Enjoy the tactile contrast of warm, savory filling with crisp, fresh lettuce in every bite.