Prep all of your ingredients: Cut up the chicken and vegetables so that they are ready for stir-frying. Place the sliced chicken in a bowl add 1 tablespoon of oil and 1 teaspoon of fish sauce. Mix this together and let it sit for 5 to 10 minutes.
Semi-cook the chicken: Get out a wok, or skillet, add 1 tablespoon of oil to it and place it over high heat. Once its hot add the chicken and let them cook for 2 to 3 minutes just to get it semi-cooked. Then transfer the semi-cooked chicken to a plate and set aside till later. Also depending on the size of your wok/skillet you might want to cook the chicken in batches so that they aren’t overcrowded and “stew”.
Make the sauce: Add the remaining 2 Tablespoons of oil to your wok/skillet and turn the heat down to medium. Then toss in the red curry paste and garlic. Stir and let this cook for 1 minute. Then toss in the tablespoon of brown sugar stir it in, and let it continue to cook for another minute. Finally toss in the kaffir lime leaves and chicken stock, stirring it all together.
Add the vegetables: Toss the carrots, bell peppers, and green beans into the wok/skillet and stir fry for 2 to 3 minutes.
Return the chicken: Return the semi-cooked chicken to the wok/skillet. Then continue to stir fry everything for about 2 more minutes, or until the vegetables are as soft as you prefer and the sauce is a thick as you like.
Plate the pad prik king along with some rice to soak up the delicious sauce. Enjoy!