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, stirring occasionally, until browned. Remove the sausage from the skillet and set aside.
In the same large pot, melt the unsalted butter over medium heat. Add the chopped onion, celery, and carrots. Cook for 5-6 minutes until the vegetables are softened and the onion is translucent.
Add the minced garlic and cook for 1 minute, stirring frequently to avoid burning.
Sprinkle the all-purpose flour over the vegetables and stir well to coat. Cook for 2 minutes to remove the raw flour taste, stirring constantly.
Slowly whisk in the chicken broth, making sure to incorporate the flour mixture smoothly without lumps.
Add the diced potatoes, dried thyme, smoked paprika, black pepper, and kosher salt. Stir to combine.
Bring the mixture to a boil, then reduce heat to low and simmer uncovered for 20 minutes or until the potatoes are tender.
Stir in the whole milk and heavy cream. Add the browned sausage back into the pot. Heat the soup gently over low heat for 5 minutes, stirring occasionally. Do not boil after adding the milk and cream to prevent curdling.
Taste and adjust seasoning with additional salt and pepper if needed.
Remove from heat and stir in the chopped fresh parsley.
Ladle the chowder into bowls and serve hot.