Combine vegetable broth, lemon grass, vegetable bouillon, and star anise pods in a saucepan and bring to a boil. Reduce heat and let simmer until flavors are combined, 30 to 45 minutes. Remove lemon grass and star anise with a slotted spoon and discard.

Place rice noodles in a bowl and cover with hot water to soften, about 10 minutes. Drain and cut into shorter pieces with kitchen shears; divide noodles equally between soup bowls. Fill bowls with hot broth to cover noodles.

Place bean sprouts, mushrooms, limes, cilantro, basil, and green onions into separate bowls. Place teriyaki sauce, soy sauce, chile paste, and sesame oil in separate bowls. Serve soup alongside garnishes and flavorings.