Heat 2 tablespoons of olive oil in a large pot over medium heat until shimmering. Add the sliced kielbasa and cook for about 5 minutes, stirring occasionally, until it is nicely browned and has rendered its flavorful juices. Remove the kielbasa from the pot and set it aside.

In the same pot, add diced onion, minced celery, and sliced carrots. Sauté for 5-7 minutes until the vegetables begin to soften and the onion turns translucent.

Add minced garlic and stir gently for about 30 seconds, being careful not to let it burn.

Sprinkle 2 tablespoons of flour over the sautéed vegetables, stirring constantly for 1 minute until the mixture turns a light golden color.

Add diced russet potatoes, dried thyme, smoked paprika, kosher salt, and black pepper. Stir well to coat the potatoes evenly.

Pour in 4 cups of low-sodium chicken broth and enough water to cover the potatoes, about 1-2 cups. Stir and increase heat to bring to a gentle boil. Reduce to low and let simmer for 15-20 minutes until the potatoes are fork-tender.

Return the browned kielbasa to the pot and let it simmer for an additional 5 minutes.

Reduce the heat to low and stir in 1 cup of heavy cream and ½ cup of sour cream. Cook for an additional 3-5 minutes.

Taste the soup and adjust seasoning with more salt and pepper as needed.

Ladle the soup into bowls and garnish with freshly chopped parsley.