Combine the chicken, carrots, bay leaf and a pinch of salt in a medium saucepan. Add 3 cups stock and bring to a boil; then reduce the heat to low, cover and cook until the chicken is just firm, about 20 minutes.
Meanwhile, heat the butter in another saucepan over medium-low heat. Add the onion, sugar and 1 teaspoon salt; cook until the onion is soft, 5 minutes. Add the curry powder and cook for 1 minute. Add the rice and the remaining 3 cups broth. Increase the heat to medium, cover and simmer until the rice falls apart, 15 to 20 minutes.
Remove the chicken from its broth; discard the skin and bones and shred the meat into pieces. Return the shredded chicken to the same broth.
Puree the rice mixture with an immersion blender until smooth (or use a regular blender, then return to the pan). Pour in the shredded chicken and broth, stirring gently to combine; bring to a simmer. Toss in the chopped herbs and serve the soup with lemon wedges.
*Always use caution when blending hot liquids*