Melt the butter in a Dutch oven over medium-high heat. Sprinkle the chicken thighs evenly with 1/2 tsp salt and 1/4 tsp pepper. Add the chicken thighs to the pan; saute for 3 minutes on each side or until browned. Remove the chicken thighs from the pan.
Add the onion, carrot, and miso to the pan; saute for 2 minutes, stirring occasionally. Add wine; cook for 1 minute, scraping the pan to loosen browned bits.
Chop the chicken thighs into bite-sized pieces; return chicken thighs to the pan. Tie twine around the herbs to secure. Add the herbs, stock, celery, and chicken breast to the pan; bring to a boil. Reduce heat, and cook for 5 minutes.
Add the remaining 1/4 tsp salt, 1/4 tsp pepper, and pasta; simmer for 2 minutes, or until the pasta is done. Discard the herbs. Sprinkle with green onions.