Heat oil in a large heavy pot over medium-high heat. Add onion; cook, stirring occasionally, until tender, about 5 minutes. Add garlic; cook, stirring constantly, until fragrant, about 30 seconds. Stir in broth, water, potatoes, parsnips, rosemary, and salt; bring to a boil. Reduce heat to medium-low; cover and cook, stirring occasionally, until the vegetables are tender, about 15 minutes. Let cool for a few minutes and then immersion blend soup until thick and smooth.