Combine the chicken, carrots, bay leaf and a pinch of salt in a medium saucepan. Add 3 cups broth and bring to a boil; immediately 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 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.
Photography by Antonis Achilleos