Heat the sesame oil in a large pot over medium heat. Add the chicken pieces and season with salt and pepper. Cook until lightly browned on all sides, about 5 minutes.
Add the onion, garlic, and ginger to the pot. Stir and cook for 2 minutes until the onion softens.
Pour in the soy sauce and chicken broth. Scrape the bottom of the pot to loosen any browned bits.
Add the daikon and carrots. Bring the mixture to a simmer.
Reduce heat to low, cover the pot, and cook for 25 minutes until the chicken is tender and the vegetables are soft.
Taste and adjust salt or pepper if needed. Remove from heat and let it rest for a few minutes before serving.
Ladle into bowls and top with sliced green onions.