Take a large wok. Add the cooking oil in it and set it over medium-high heat.
Add the peppers and onion. Simmer, uncovered, for 5 minutes or until the veggies are tender.
Cook for 30 seconds after adding the garlic. Put the veggies on hold.
If necessary, add extra oil to the pan along with the chicken pieces. Cook until the exterior of the chicken is browned. Later, it will cook through in the sauce. Put the chicken on hold.
To extract the oils from the paste, return to the pan and scoop the paste in, stirring.
Add the cooked chicken and veggies to the paste and stir. Add another minute of cooking time.
Stir the fish sauce, lime juice, brown sugar, and peanut butter.
Keep cooking, stirring often, for three minutes.
After reducing the heat to medium, add the coconut milk. Stir with a whisk.
The chicken should be cooked through and the sauce should have a slight thickening after 5 to 7 minutes of cooking.
Before serving, add the Thai basil leaves.