Heat the olive oil in a large stock pot over medium-high heat. Add the sliced kielbasa sausage and cook for 3 to 4 minutes, or until lightly browned. Remove the sausage from the pot and transfer it to a separate plate. Leave the rendered grease and drippings in the pot.
Sauté the vegetables.
Add the diced onion, carrots, and celery to the same pot. Sauté for 3 to 4 minutes, or until the vegetables begin to soften.
Add the garlic.
Stir in the minced garlic and cook for 1 minute, or until fragrant.
Add the flour.
Sprinkle the all-purpose flour over the vegetables. Whisk or stir until the flour is evenly combined with the vegetables and drippings. Cook for 1 minute to remove the raw flour taste.
Add the chicken broth.
Slowly pour in the chicken broth while whisking continuously. Scrape the bottom of the pot to release any browned bits and incorporate them into the soup.
Add the sausage, potatoes, milk, and seasonings.
Return the browned kielbasa to the pot. Add the frozen cubed hash brown potatoes, red chili flakes, milk, salt, and black pepper. Stir until all ingredients are evenly combined.
Simmer the soup.
Bring the mixture to a boil. Cover the pot, reduce the heat to low, and cook for 8 to 10 minutes, or until the potatoes are fork tender.
Add the cheese.
Remove the pot from the heat. Stir in the shredded cheddar cheese until fully melted and evenly incorporated into the soup.
Adjust the seasoning.
Taste the soup and add additional salt or pepper if needed.
Serve.
Ladle the soup into bowls and serve hot.
Notes
To make this recipe gluten-free, replace the all-purpose flour with a gluten-free all-purpose flour blend or cornstarch slurry.Use certified gluten-free kielbasa sausage, as some sausages may contain gluten-based fillers, binders, or flavorings.Confirm that the chicken broth, frozen cubed hash brown potatoes, milk, cheddar cheese, red chili flakes, salt, pepper, garlic, onion, carrots, celery, and olive oil are gluten-free.If using pre-shredded cheddar cheese, check the label for gluten-containing anti-caking agents or cross-contamination warnings.Use clean cookware, cutting boards, knives, measuring tools, and serving utensils to prevent cross-contamination.Serve with gluten-free bread, gluten-free crackers, or a gluten-free side salad if desired.