Heat the olive oil and butter in a medium Dutch oven or heavy-bottomed soup pot over medium-high heat.
Once the butter has melted, add the chopped red onion and minced garlic.
Sauté for 1–2 minutes, stirring frequently, until the onion begins to soften and the garlic becomes fragrant.
Add the all-purpose herb seasoning and smoked paprika. Stir for about 30 seconds to distribute the spices.
Add the cubed potatoes and toss until lightly coated with the seasonings.
Pour in the 4 cups of vegetable broth plus the additional 2 tablespoons being used in place of cooking wine.
Increase the heat and bring the mixture to a boil. Allow it to boil gently for 1–2 minutes.
Reduce the heat to low or medium-low and simmer for 15–20 minutes, or until the potatoes are completely tender.
For a naturally thicker soup, continue simmering for approximately 5–10 additional minutes, allowing some of the potatoes to soften enough to break apart.
Gently mash a portion of the potatoes against the side of the pot with a spoon or potato masher while leaving plenty of chunks intact.
Reduce the heat to low and stir in the heavy cream.
Add the chopped kale, if using, and simmer gently until it begins to soften.
Add the freshly grated sharp cheddar gradually, stirring after each addition until completely melted.
Avoid vigorously boiling the soup after adding the dairy and cheese.
Taste the Hearty Cheddar Garlic Herb Potato Soup and adjust the seasoning as necessary.
Remove from the heat and ladle into bowls.
Garnish with fresh parsley or sliced green onions and serve warm with crusty bread if desired.