Begin by dicing the onion finely, chopping the carrots into bite-sized pieces, and dicing the celery. Mince the garlic cloves until finely chopped, and then cube the red potatoes into 1/2-inch pieces. Set all vegetables aside.

In a large pot, heat over medium-high, adding the sausage. Cook for approximately 10-12 minutes, breaking it apart with a spatula until it's fully crumbled and browned with a crispy edge. Once browned, remove the sausage from the pot but reserve the flavorful fat.

Using the same pot, melt the 3 tablespoons of butter in the reserved sausage fat over medium heat. Once melted, add the diced onions, carrots, and celery, cooking for about 5 minutes until softened and fragrant. Stir in the minced garlic and cook for another minute.

Sprinkle 3 tablespoons of flour over the sautéed vegetables while stirring constantly for about 2 minutes to ensure that the flour coats the vegetables evenly and cooks through.

Slowly pour in 6 cups of chicken broth while stirring continuously to prevent lumps. Add the heavy cream, 1 teaspoon of soy sauce, and 1 1/2 teaspoons of hot sauce. Stir in the dried basil, parsley, oregano, mustard powder, pepper, and smoked paprika until combined.

Raise the heat to bring the mixture to a gentle boil, then reduce to a simmer. Add the cubed red potatoes and cook for approximately 20-25 minutes or until tender.

Once the potatoes are tender, return the browned sausage to the pot and heat everything through for about 1-2 minutes. Gradually stir in 2 1/4 cups of shredded cheddar cheese.

Ladle the soup into warm bowls and serve with crusty bread or cornbread for dipping.