Heat 1 tablespoon sesame oil in a large frying pan over medium heat. Add garlic and 1/3 of the basil. Saute until garlic is fragrant, about 30 seconds. Add onion and cook until transparent, 5 to 7 minutes.
Add chicken to the pan with remaining sesame oil and season with chile powder. Add mushrooms and bamboo shoots. Cook until the chicken is only slightly pink in the center and the mushrooms have started to lose their moisture, 4 to 5 minutes. Add curry paste and mix well.
Pour in 1/2 of the coconut milk. Stir until vegetables and chicken are evenly coated. Add peanut butter and curry powder and mix thoroughly. Cook over medium heat until the sauce thickens, stirring often to keep the sauce from burning to the bottom of the pan, 10 to 15 minutes.
Reduce heat to low and add remaining coconut milk and brown sugar. Continue to simmer over low heat until desired consistency is reached, 10 to 15 minutes more, tasting and adding more peanut butter if needed.