**Cook the Sausage:** In a large pot or Dutch oven, sauté the sausage over medium heat until browned. Remove and set aside.
**Sauté Vegetables:** In the same pot, melt the butter. Add the onion and garlic, cooking until softened and fragrant, about 3 minutes.
**Add Flour:** Sprinkle the flour over the onions and garlic, stirring constantly to make a roux. Cook for 1–2 minutes.
**Add Broth and Potatoes:** Gradually whisk in the chicken broth. Add the diced potatoes, smoked paprika, and thyme. Bring to a boil, then reduce the heat and simmer until the potatoes are tender, about 15–20 minutes.
**Incorporate Cream and Sausage:** Stir in the heavy cream and cooked sausage. Simmer for another 5 minutes to heat through.
**Season and Finish:** Season with salt and pepper to taste. If desired, stir in the shredded cheddar cheese until melted.
**Serve:** Ladle the chowder into bowls, garnish with fresh parsley, and serve warm.