Heat oil in a large pot over medium heat. Add jalapeño, garlic, ginger, and lime zest; cook and stir for 1 minute. Add shredded chicken and stir until well blended, about 30 more seconds.
Add coconut milk, chicken stock, curry paste, soy sauce, fish sauce, brown sugar, and basil; stir well. Bring to a simmer, stirring occasionally.
Add ramen noodles, snow peas, and bell pepper; cook until noodles are al dente and the vegetables are crisp-tender, 3 to 5 minutes.
Serve hot garnished with cilantro.
