In a medium saucepan, add the chicken stock, lemongrass, garlic clove, ginger, cilantro, chicken breast and large pinch of salt. Make sure the liquid covers the chicken. If it doesn’t, add more stock. Bring the mixture up to a boil; turn off the heat, cover and let sit for 20 minutes, or until the chicken is completely cooked through.
Remove the chicken and set aside on a separate platter. Reserve the poaching liquid.
Over medium heat, in a separate saucepan, heat 1-tablespoon coconut oil. Add sliced shallots, and sauté until they are soft and they just begin to brown, about 5 minutes.
Add the curry paste, and sauté for about 1 minute.
Use a fine mesh sieve to strain the chicken poaching liquid into the shallot/curry paste mixture. Add 3 kaffir lime leaves, and allow to simmer gently.Meanwhile, de-stem and de-string the green beans and snow peas, and cut into half inch pieces.Bring a small pot of salted water to a boil, add the veggies, and drain as soon as they come back up to a boil.Add coconut milk, shredded chicken, blanched veggies, lime juice, and coconut sugar to the soup.Taste for seasoning, garnish with cilantro and serve with extra lime on the side.