Heat the olive oil and butter in a large pot over medium heat until the butter has completely melted.

Add the finely chopped onion and sauté for about 5 minutes, stirring occasionally, until softened and translucent.

Stir in the minced garlic, dried thyme, dried parsley, and smoked paprika. Cook for about 1 minute, just until the garlic and herbs become fragrant.

Add the diced potatoes and pour in the chicken or vegetable broth. Bring the mixture to a boil, then reduce the heat and simmer for approximately 20 minutes, or until the potatoes are very tender.

Use an immersion blender to partially blend the soup directly in the pot. Leave some potato pieces intact for a hearty texture. Alternatively, carefully blend about half of the soup in a countertop blender and return it to the pot.

Reduce the heat to low. Stir the whole milk and heavy cream into the Cheddar Garlic Herb Potato Soup and warm gently without allowing it to boil.

Add the shredded sharp cheddar gradually, stirring continuously after each addition until the cheese is completely melted and the soup is smooth.

Season with salt and freshly ground black pepper to taste. Add a little more thyme or parsley if you prefer a stronger herb flavor.

Ladle the soup into bowls and serve hot with fresh parsley and additional shredded cheddar, if desired.