Heat a wok or large frying pan over medium-high heat. When hot, add the sesame oil, and coat the pan. Stir in 3 tsp. of the garlic, 6 tsp. of the ginger, and the red onion and fry together for 1 minute. Add the ground chicken and shiitake mushrooms next and continue to stir together until they are lightly browned, about 2 to 4 minutes. Then stir in the soy sauce, hoisin sauce, and 3 tsp. of the Sriracha. Simmer all the ingredients for 2 minutes, or until the meat is cooked through. Let the mixture cool and then add the lime juice. Meanwhile, place the peanut butter, coconut milk, 1 tsp. of the ginger, 1 tsp. of the garlic, 1 tsp. of the Sriracha sauce, and the fish sauce into a medium size bowl and mix will. To assemble the lettuce wraps, spoon a bit of the chicken filling onto each lettuce cup and drizzle with desired amount of sauce and garnish with cilantro, cucumber and carrots.