Heat oil in a large pot over medium-high heat. Stir in mushrooms and zucchini; cook, stirring often, until the vegetables are slightly softened, 3 to 5 minutes. Stir in garlic paste; cook, stirring constantly, until fragrant, about 1 minute. Add water, marinara and salt; bring to a boil over medium-high heat. Add noodles and stir to separate, about 30 seconds. Cook, stirring occasionally, until the noodles are just cooked through but not completely soft, 8 to 10 minutes. Add spinach; cook, stirring occasionally, until just wilted, about 1 minute.
Meanwhile, combine ricotta, shredded cheese and Parmesan in a small bowl.
Divide the soup among 4 bowls. Top each serving with a dollop of the ricotta mixture.
