In a large pot or Dutch oven, heat a medium skillet over medium heat. Add the sliced smoked sausage and cook for 5-7 minutes until browned on both sides. Remove sausage from skillet and set aside.
In the same large pot or Dutch oven, melt the butter over medium heat. Add the diced onion, celery, and carrots. Cook, stirring occasionally, for about 5 minutes until vegetables are softened.
Add the minced garlic and cook for 1 minute until fragrant.
Sprinkle the flour over the vegetables and stir constantly for 2 minutes to form a roux.
Slowly whisk in the chicken broth to avoid lumps. Stir in the dried thyme and smoked paprika.
Add the diced potatoes and bring the mixture to a boil. Reduce heat to medium-low and simmer for 15 minutes or until potatoes are tender.
Stir in the browned sausage, whole milk, and heavy cream. Heat the soup gently for another 5-7 minutes, stirring occasionally. Do not boil after adding milk and cream to prevent curdling.
Season the chowder with salt and black pepper to taste.
Remove from heat and ladle the chowder into bowls. Garnish with chopped fresh parsley before serving.