In a large pot, combine 2 tablespoons of unsalted butter and 1 tablespoon of olive oil over medium heat.

Once the butter melts, add 1 finely chopped onion, 1 small diced carrot, and 1 small diced celery stalk. Sauté for 5–7 minutes until softened and translucent.

Stir in 2 cloves of freshly minced garlic and cook for an additional 30 seconds until fragrant.

Sprinkle 1/4 cup of all-purpose flour over the sautéed vegetables. Stir constantly for 1–2 minutes to form a roux.

Slowly whisk in 4 cups of chicken broth, then add 2 cups of whole milk and 1/2 cup of heavy cream, stirring continuously until smooth.

If using, add diced potatoes and let the soup simmer on low for 10–15 minutes.

Reduce heat to low and stir in 3 cups of freshly shredded sharp cheddar cheese until melted and smooth.

Add 1 tablespoon of Dijon mustard, 1/2 teaspoon of smoked paprika, and salt and black pepper to taste. Add optional add-ins if desired.

Ladle the soup into bowls and serve hot, optionally with extra cheese or chives.