- 2 teaspoons sesame oil, divided
- 1 (4 inch) piece fresh ginger, peeled and chopped, or to taste
- 3 quarts chicken broth
- 1 large red onion, diced
- 2 cups sliced carrots
- 1 tablespoon curry powder
- 1 tablespoon ground ginger
- 1 tablespoon cayenne pepper
- salt and ground black pepper to taste
- 1 jalapeno pepper, finely chopped
- 6 limes, juiced, divided
- 1 (9 ounce) package udon noodles
- 4 skinless, boneless chicken breast halves, cubed
- 1 leek, cut into matchstick-size pieces
- 1 green onion, finely chopped
- Heat 1 teaspoon sesame oil in a large pot over low heat; cook and stir ginger in the hot oil for 10 minutes. Pour chicken broth over ginger, cover pot, and simmer for 30 minutes.
- Stir onion and carrots into broth and simmer until carrots are tender, about 10 minutes. Gradually add curry powder, ground ginger, cayenne pepper, salt, and black pepper to broth; stir in jalapeno pepper and half the lime juice. Simmer broth over low heat, stirring about every 15 minutes, until flavors have blended, about 1 hour.
- Fill a large pot with lightly salted water and bring to a rolling boil. Drop udon in a few noodles at a time and return to a boil. Cook uncovered, stirring occasionally, until the pasta has cooked through, but is still firm to the bite, 10 to 12 minutes; drain.
- Heat 1 teaspoon sesame oil in a skillet over medium heat; cook and stir chicken in the hot oil until no longer pink in the center, about 10 minutes. Transfer chicken to broth and stir leek and green onion into broth; simmer for 5 to 10 more minutes. Remove pot from heat.
- Portion udon noodles into each serving bowl; ladle broth over noodles. Add remaining lime juice to each serving.