Add olive oil to a large, heavy-bottomed pot and set over medium-high heat. Season the chicken with salt and pepper. Add chicken and stir fry for about 6 minutes, or until golden brown. Remove from the pan with a slotted spoon and set aside. Chicken will not be cooked through.
Add onion to the same pot and cook for 6 to 8 minutes, or until the onions are softened and golden brown. Add ginger, garlic and jalapeño (if using) and cook for 1 minute more, or until very fragrant. Season with ½ teaspoon salt and ¼ teaspoon pepper.
Add the green curry paste, stirring with a wooden spoon to coat all of the aromatics with curry paste. Add the coconut milk, and bring to a simmer.
Add green pepper, cauliflower and chicken to the pot and cover and cook at a simmer for 5 to 7 minutes, or until the vegetables are tender and the chicken is cooked through.
Remove from heat and stir in lime juice, cilantro and basil before serving with steamed rice or noodles.
