Heat coconut oil in a large pot over medium-high heat. Add bok choy; cook and stir until wilted, 3 to 5 minutes. Stir in garlic and ginger; cook until fragrant, about 1 minute. Add carrots, five-spice powder, and cumin.

Pour vegetable broth into the pot. Bring the soup to a boil. Add noodles; reduce heat and simmer until noodles soften, about 3 minutes. Stir in bean sprouts and scallions. Remove soup from heat; let stand until flavors combine, about 5 minutes.