In a large pot, heat olive oil over medium heat. Add the chopped onion and diced celery, sautéing until softened, about 5 minutes.
Stir in the minced garlic and cook for an additional 1-2 minutes until fragrant.
Add the diced potatoes, vegetable broth, dried thyme, and dried rosemary to the pot. Bring to a simmer and cook for 15-20 minutes, or until the potatoes are tender.
Once the potatoes are cooked, use an immersion blender to puree the soup until smooth. If you don’t have an immersion blender, carefully transfer the soup in batches to a countertop blender.
After the soup is blended, return it to the pot (if needed) and stir in the heavy cream and grated Parmesan cheese, mixing well until the cheese is melted and the soup is creamy.
Season with salt and pepper to taste and heat the soup for an additional 5 minutes on low heat.
Serve hot, garnished with fresh parsley and an extra sprinkle of Parmesan if desired.