In the bowl of a food processor, combine galangal, garlic, Thai chilies, shallots, 1 cup cilantro leaves, coconut milk, chili sauce and salt and pepper to taste. Pulse on high for 30 seconds or until mixture is a smooth puree. Place chicken in a bowl and pour marinade over chicken, turning the chicken several times to coat. Cover and refrigerate for 24 hours.
Preheat oven to 400 degrees F.
Remove chicken from marinade and pat dry. Season with salt and pepper. In a large oven-safe saute pan on medium high heat, add canola oil and sear chicken, skin side down. Let chicken cook, undisturbed, for 3 to 4 minutes or until browned well. Place pan in oven for 12 minutes or until chicken is cooked through. Remove chicken from pan and set aside until cool enough to handle. Meanwhile, in the same saute pan, add chicken stock and Buddha Chicken Chili Sauce and bring to a simmer, scraping the bottom of the pan with a wooden spoon to incorporate any browned bits. Let mixture simmer for 6 to 8 minutes. Add butter and stir to incorporate.
While the sauce is simmering, French the chicken pieces: using a kitchen towel, hold the wing tip of the chicken and scrape the meat toward the breast until the bone is bare. Repeat the process with the drumstick and thigh portion and set aside.
Using square plates, shingle slices of peeled sliced lime, top with some Choi Sum, place the chicken on top, and drizzle with more sweet Thai chili sauce, if desired.
In a medium non-reactive bowl, dissolve sugar in lime juice and mix well. Add chili sauce and mix to combine. Place the mixture into the bowl of a food processor and pulse until smooth, about 15 seconds.
In a medium pot, bring 4 quarts of salted water to a boil. Place ice cubes in a medium bowl and cover with cold water. When water is boiling, add choi sum and cook for 10 seconds. Remove from water and add to bowl with ice cubes to stop the cooking process. Once cooled, remove from bowl and place onto paper towel lined plate to drain excess water.
Just before serving, heat oil in a medium saute pan over medium heat. Add garlic and onion and sweat for 15 seconds. Add choi sum, chili sauce, sugar, and lime juice, and continue to cook for 30 seconds. Drain on a paper towel-lined plate before serving.