Heat the olive oil and butter in a medium Dutch oven over medium-high heat.
Add the minced garlic and chopped red onion. Sauté for 1–2 minutes, until the onion is translucent and the garlic is fragrant.
Stir in the smoked paprika and all-purpose seasoning blend.
Add the cubed potatoes and stir well to coat them with the seasoned onion and garlic mixture.
Pour in the vegetable stock and bring the soup to a boil. Let it boil for 1–2 minutes.
Reduce the heat to low and simmer for 15–20 minutes, or until the potatoes are tender.
For a naturally thicker Cheddar Garlic Herb Potato Soup, continue simmering for about 10 additional minutes, allowing some of the potatoes to break down into the broth.
Stir in the heavy cream, chopped kale if using, and white cooking wine.
Add the freshly grated sharp cheddar a little at a time, stirring frequently until completely melted and the soup is creamy.
Remove from the heat and taste for seasoning. Adjust if needed.
Ladle into bowls and garnish with freshly chopped parsley or green onions. Serve with crusty bread if desired.