Remove and discard skin and bones from the chicken. Tear into bite-sized pieces and place in a large stockpot. Add the chicken broth, coconut milk, carrots, rice noodles, corn kernels, soy sauce, green curry paste. kosher salt, cayenne pepper, and cilantro. Stir to combine and bring to a low boil over medium-high heat; reduce heat. Simmer for about 8-10 minutes, or until carrots are starting to turn tender.
Ladle into bowls and add more cilantro, if desired.