Cook the Sausage: Heat a large pot over medium-high heat. Add sausage and sear for 1 minute. Crumble with a wooden spoon and cook until browned. Transfer sausage to a paper towel-lined plate, leaving about 1 tablespoon of grease in the pot. Add olive oil if needed.

Sauté Vegetables: In the same pot, melt 1 tablespoon butter. Add diced carrots, celery, and onion. Sauté for 5–7 minutes (or 7–10 minutes for larger veggies). Add garlic and cook for 30 more seconds.

Cook Potatoes: Stir in chopped potatoes, dried basil, dried parsley, salt, and pepper. Pour in chicken stock and bring to a boil. Reduce heat to medium-low, cover, and cook for 15–20 minutes until potatoes are fork-tender.

Make the Cream Sauce: While the potatoes cook, melt 4 tablespoons butter in a separate medium pot over medium heat. Whisk in flour and cook for 1 minute. Slowly pour in milk, whisking constantly until smooth. Cook until the mixture thickens and gently boils. Stir in heavy cream and remove from heat.

Finish the Soup: Once potatoes are tender, stir in the milk/cream mixture. Turn off heat and add shredded cheese, a handful at a time, stirring gently until melted. Stir in sour cream, then return the sausage to the pot. Adjust seasoning with salt and pepper to taste.

Serve: Serve warm with hearty buttered bread, if desired.