Preheat the oven to 400 degrees F. Line a baking sheet with foil. Toss the cauliflower and parsnips with the olive oil and sprinkle with salt and pepper.
In a large Dutch oven, melt the butter over medium heat. Add the leeks and sauté about 6 minutes. Add the roasted veggies and potato.
Stir in the broth and bring to a boil. Reduce heat and allow to simmer for 20 minutes for the flavors to blend. When ready, use an immersion blender to puree the soup.
Stir in the ham, milk, vinegar, nutmeg, cayenne and cheese. Stir over low not allowing the soup to boil. Season with salt and pepper. Ladle into bowls and garnish with freshly minced chives.