Heat sesame oil in a large pot over medium heat. Add ginger and garlic, sautéing for 1–2 minutes until fragrant.
Pour in the vegetable broth, soy sauce, rice vinegar, and chili paste. Bring to a gentle boil.
Add mushrooms and carrots, reducing heat to simmer for 8–10 minutes until tender.
Stir in the spinach, allowing it to wilt. Adjust seasoning to taste.
Divide cooked noodles into bowls, then ladle the hot broth and vegetables over them.
Garnish with green onions and sesame seeds before serving.
