Prepare the sauce by whisking together the hoisin sauce, soy sauce, rice wine vinegar, oyster sauce, sesame oil, brown sugar, and sriracha in a small bowl until the sugar dissolves completely. Set the sauce aside so the flavors can meld together while you prepare the filling, about 5 minutes.
Heat the vegetable oil in a large skillet or wok over medium-high heat until it shimmers and a drop of water sizzles on contact, about 2 minutes. Add the ground chicken and break it apart with a wooden spoon or spatula, cooking until it's no longer pink and begins to brown slightly, about 4-5 minutes.
Push the cooked chicken to the sides of the pan, creating a well in the center. Add the minced garlic and ginger to the center and cook until fragrant and golden, stirring constantly for about 30 seconds to prevent burning.
Add the finely chopped water chestnuts and diced shiitake mushrooms to the pan, stirring everything together with the chicken. Cook for 3-4 minutes until the mushrooms soften and release their moisture, and the water chestnuts become slightly tender while maintaining their signature crunch.
Pour the prepared sauce over the chicken mixture and add the white parts of the sliced green onions. Stir everything together thoroughly, allowing the sauce to coat all the ingredients evenly and simmer for 2-3 minutes until it thickens slightly and becomes glossy.
Remove the pan from heat and stir in the green parts of the sliced green onions, reserving a small amount for garnish. Taste and adjust seasoning if needed, adding more soy sauce for saltiness or brown sugar for sweetness.
Arrange the clean, dry butter lettuce leaves on a serving platter, creating cup shapes that will hold the filling. The leaves should be intact and large enough to hold about 2-3 tablespoons of filling each without tearing.
Spoon the warm chicken mixture into the center of each lettuce cup, being careful not to overfill them. Garnish with toasted sesame seeds, crispy rice noodles, fresh cilantro, and the reserved green onion slices for an authentic P.F. Chang's presentation that's both beautiful and delicious.