Heat oil and butter over medium-high heat in a Dutch oven or other soup pot.
Add the onion, reduce heat to medium-low and cook for 5-7 minutes or until beginning to soften.
Add the garlic and cook briefly, 10-15 seconds or until fragrant.
Add the wine and bring to a boil. Boil for approximately 30 seconds.
Add the potatoes, cauliflower and 4 cups of the chicken broth. Bring to a boil then reduce heat to low and simmer 20-25 minutes or until potatoes and cauliflower are very tender.
Remove from the heat and stir in the cream.
Add the cheese by the handful, stirring well after each addition.
Puree with an immersion blender until smooth or in a food processor or blender, being careful with hot liquids. If the soup is extremely thick, add additional chicken broth as needed to thin it out.
Season to taste with salt and white pepper.
Serve garnished with optional bacon, chives, paprika or roasted cauliflower florets.