1: To make the peanut sauce, whisk together peanut butter, soy sauce, lime juice, brown sugar, chili garlic sauce and ginger in a small bowl. Whisk in 2-3 tablespoons water until desired consistency is reached; set aside.
2: Heat vegetable oil and sesame oil in a large skillet over medium high heat. Add ground chicken, mushrooms, carrot and shallot. Cook until browned, about 5-7 minutes, making sure to crumble the chicken as it cooks; drain excess fat.
3: Stir in garlic and ginger until fragrant, about 1 minute.
4: Stir in hoisin sauce, chili garlic sauce and fish sauce until heated through, about 30 seconds. Remove from heat; stir in cilantro.
5: To serve, spoon several tablespoons of the chicken mixture into the center of a lettuce leaf, taco-style, drizzled with peanut sauce.
