In a large heavy pot or Dutch oven, heat oil over medium-low heat. Add onion and garlic; cover and cook, stirring occasionally until onion has softened, about 3 minutes. Add potato and broth, and raise heat to high; bring the mixture to a boil.
Reduce heat to medium; cover and simmer until potato is tender, about 10 minutes. Stir in the parsley and cook, uncovered, until parsley is wilted, about 2 minutes.
Working in batches, puree mixture in blender until smooth; season with salt and pepper. Ladle into individual soup bowls and garnish, if desired, with one of the optional garnishes. Serve immediately.