Heat ½ cup coconut milk in a large pan over medium heat. Simmer until the fat separates and bubbles appear on the surface.
Stir in green curry paste and cook until fragrant, about 1-2 minutes.
Add chicken pieces and coat thoroughly in the curry mixture. Cook briefly for 2-3 minutes.
Pour in remaining coconut milk, chicken stock, palm sugar, fish sauce, and lime leaves.
Bring to a simmer and cook until chicken is fully cooked through, about 8-10 minutes.
Add bamboo shoots, red bell pepper, and Thai basil leaves. Heat through for 2-3 minutes.
Serve immediately over jasmine rice.