In a warm skillet over medium-high heat, put olive oil, then lightly fry sliced chicken breast. Don't overcook it! As this will make the meat become tough. Should take no more than 4 minutes. Set meat aside.
In the same pan, add oil as needed, then add the red curry paste, stir until fragrant. Add fish sauce and coconut sugar, stir well. Then add the coconut milk. Mix the ingredients together.
Add the vegetables in the order that it's written above. Give it about two minutes each. This will ensure all the vegetables cook at the same time. Add the kaffir lime leaves last.
Put the chicken back in the curry mixture. Season to taste adding fish sauce and/or sugar as desired.
Notes
You can use frozen kaffir lime leaves, although, I have found mine fresh at Amazon.
Check out my other blog post on how to freeze kaffir lime leaves for future use.
If you can't find green string beans (which can be found in Asian markets, you can substitute regular green beans).
You can use dried shiitake mushrooms in place of fresh ones. Prepare as instructed on package.
You may substitute dried shiitake mushrooms. Soak them in warm water for about 5 minutes first, then remove hard stems).
Adjust the coconut sugar and fish sauce as desired. Start with 2T, then add 1T at a time to get to your desired flavor profile.