Heat the oil on medium low heat in a saute pan. Add the chicken, garlic, salt and pepper and cook for about 4 minutes or until just cooked. Remove chicken on to a plate, keep warm.
Add the green beans to the remaining oil and saute for about 3 minutes. Transfer to plate. Next, saute the bell peppers, onions, and carrots together for just 1 minute. Add a few extra drops of oil in between, if necessary. Transfer to the same plate as green beans.
In the same saute pan, add the coconut milk, green curry paste, ginger root, lime zest, lime juice, dried Thai chillies, light brown sugar, turmeric, and red pepper flakes. Bring all of this to a light simmer. Continue to cook until the curry reduces to about half. Add the chicken and all of the vegetables back into the same pot and heat all the way through. Sprinkle with basil leaves. Serve warm with jasmine rice!
Notes
The dried Thai red peppers can be omitted depending on your spice preference. If you'd like to get some of the flavor, cut off the tops and remove the seeds. This should help produce the flavor without bringing too much heat.