Step 1: Heat olive oil in a large pot or Dutch oven over medium heat. Add chopped onion and cook until softened and translucent, about 5 minutes.
Step 2: Add minced garlic, diced carrots, and diced celery to the pot. Sauté for another 5-7 minutes until vegetables begin to slightly soften.
Step 3: Stir in the diced potato, broccoli florets, and cauliflower florets. Pour in the vegetable broth. Bring the mixture to a boil, then reduce heat, cover, and simmer for 20-25 minutes, or until all vegetables are very tender.
Step 4: Carefully transfer about two-thirds of the soup to a blender and blend until smooth. Alternatively, use an immersion blender directly in the pot until the desired consistency is reached.
Step 5: Return the blended soup to the pot (if using a regular blender). Stir in the heavy cream. Season generously with salt and freshly ground black pepper to taste. Heat gently until warmed through, but do not bring to a boil.
Step 6: Ladle the creamy vegetable soup into bowls. Garnish with fresh chopped parsley and serve hot with crusty bread or a side salad.