Remove skin and fat from the chicken parts. Cut breasts into three pieces and thighs into two. Sprinkle adobo seasoning all over the chicken and allow it to penetrate the chicken for at least thirty minutes.
Combine in a bowl one cup of coconut milk (save the rest for later), oyster sauce, soy sauce, bay leaves, ginger, 4 Tbs. white pepper, chopped red onion, garlic and jalapeno.
Stir the ingredients in Step 2 well, and put half the mixture into a stainless-steel or enamel saucepan big enough to hold all the chicken. Add the chicken, then top with the remaining Step 2 ingredients.
Bring the saucepan to a light boil and hold it there for 20 minutes.
Stir in the brown sugar, lemon/orange juice, and about half of the vinegar.
Lower the heat to a simmer and cook for another 20-25 minutes, until the chicken begins to fall away from the bone.
Remove the chicken. Remove and discard the bay leaves. Pour all the pan contents into a food processor and process to a rough puree. Add about half the green onions and puree until smooth. Taste the sauce and add more vinegar and white pepper and salt to your taste.
Return the sauce to the pan. Stir in the remaining coconut milk. Bring to a simmer for about three minutes, then return the chicken to the saucepan. Spoon the sauce over the chicken and cook about another ten minutes.