Crumble chorizo into a 4-quart Dutch oven over medium heat; add garlic. Cook, stirring, until chorizo is browned, about 5 minutes; drain of fat.
Stir the broth, salsa, chipotle, oregano and cumin into Dutch oven. Raise heat to medium-high; heat to a boil. Lower heat to a simmer. Cover; cook 15 minutes. Stir in vermicelli and zucchini; cook, uncovered, until vermicelli is tender but firm, 5-10 minutes. Stir in 1/3 cup of the mozzarella and cilantro. Transfer to a warm serving dish; sprinkle with the remaining 1/3 cup cheese; garnish with additional cilantro.