Place an 8-quart stockpot over medium heat, and add the olive oil to it. Once the oil is hot, about 1 minute, add the butter. Once the butter has melted, add the ham and sear, browning on all sides, 3 to 4 minutes. Add the onions, celery, and parsnips to the pot and cook, stirring often, for 5 minutes. Once the vegetables are cooked, add the garlic to the pan and cook until fragrant, about 30 seconds. Follow with the leeks and thyme. Cook the leeks, stirring often, for 10 minutes. Pour the stock into the pot and bring the contents to a boil, then reduce to a simmer. Add the potatoes, salt, and white pepper and cook until the potatoes are tender, 20 to 25 minutes. Remove the pot from the heat, and puree the soup with an immersion blender, or in batches in a bar blender. Return the pureed soup to the stove and bring to a simmer. Add the cream to the soup and cook for 2 to 3 minutes. Taste the soup and season if necessary. Serve garnished with parsley.
Makes 4 quarts, 12 to 16 servings