Heat oil in a large saucepan over medium heat. Add garlic and 1/4 cup cilantro; cook, stirring, until the garlic is softened, 1 to 2 minutes. Add broth and water and bring to a boil. Stir in plantains and reduce heat to a simmer. Simmer until the plantains are tender and the soup is thickened, 25 to 30 minutes. Stir in the remaining 1/4 cup cilantro and season with salt and pepper. Sprinkle each serving with 1 teaspoon Parmesan cheese and garnish with a lime wedge.