Bring a dutch oven to medium-high heat. Add 1 tablespoon olive oil. Sear both sides of the chicken for 3 minutes and remove from the pot. Set aside.
Bring the heat down to medium and olive oil. Add carrots, celery, and onion. Saute for 5 minutes, then add the jalapenos and leek. Saute for another 5 minutes and add garlic and ginger. Combine all of the seasonings in a bowl. Take about ½ of the seasoning and add it to the vegetable mix. Toast for 2 minutes.
Add tomato paste to the dutch oven and stir with the vegetables. Let the tomato paste caramelize for about 3 minutes. Add the zucchini and red pepper and combine. Pour in the chicken stock and add the rest of the seasoning, the cilantro, and bay leaves. Stir well. Then add the chicken back in. Bring to a boil and then simmer for 15-20 minutes.
Remove chicken from the pot and let it rest. Add rice and stir often. Simmer for 15 more minutes until the rice is cooked. Shred the chicken and return it to the pot. Serve with fresh cilantro, lime juice, and jalapeno slices.
Notes
When you add rice to soups, you have to make sure you stir often in the first couple of minutes. The rice is prone to falling to the bottom of the pan and sticking. It can then burn and ruin the dish.
Don't overcook the chicken. Seems obvious, but only cook until it is 165 degrees and then remove. Let it cool slightly before shredding it. Otherwise, it will lose every ounce of moisture.