Remove the skin and any fat from the thighs and chop into small pieces and set aside. Cut the thigh meat into 1/3-inch pieces.
Measure out the oyster sauce, dark soy sauce, and sugar into a small bowl so that it's ready to add to the stir fry.
Prepare two frying pans (one for the egg and one for the chicken). Put the chicken skin and fat into one pan and 2 tablespoons of vegetable oil into the other.
For the pan with the chicken skin, turn the heat onto medium-high and render out the fat, stirring from time to time to prevent burning.
When the chicken skin is browned and starting to crisp, turn up the heat to high and then add the garlic and chili peppers and saute until fragrant (about 30 seconds).
Meanwhile, turn the second burner onto high heat and heat until the oil is shimmering and hot.
Add the chicken to the first pan with the garlic and chili peppers and stir fry until the chicken is cooked through.
Break an egg into the second pan and fry, spooning some oil onto the egg to help cook the top surface from time to time.
Add the sauce mix to the chicken and continue stir-frying until the sauce coats the chicken evenly.
Turn off the heat and toss the holy basil together with the chicken and plate immediately. Top your Pad Krapow Gai with the the fried egg.
Two Thai chiles will make this basil chicken fairly spicy, if you don't like a lot of heat, either cut back on the chiles, or smash (but don't chop) them so you can pick them out after cooking. If you want to make this crazy spicy, just add more chilies.