Heat oil in a large stockpot over medium. Cook onion, garlic, lemongrass, ginger, jalapeño, and cilantro stems, stirring occasionally, until lightly browned, about 5 minutes. Add wings and 10 cups water. Bring to a boil, reduce heat, and simmer until turkey meat is tender, 45–60 minutes. Strain into a large saucepan; reserve wings. Add hon-dashi and soy sauce to broth, adding more to taste if needed. Cover and keep warm. Pick meat from wings and set aside.