Heat your pot over medium heat and add the olive oil or butter. Add the sliced kielbasa and let it cook until the edges turn golden and slightly crisp. You’ll know it’s ready when the kitchen smells smoky and savory, and little browned bits form at the bottom of the pot. Those bits are pure flavor, so don’t rush this step.

Add the chopped onion directly to the pot with the kielbasa and stir well. Cook until the onion turns soft and translucent, scraping up the browned bits. Add the garlic and cook for about 30 seconds, just until fragrant. Be gentle here, as garlic burns quickly.

Sprinkle the flour over the mixture and stir until everything is coated. Cook for about a minute to remove the raw flour taste. This step helps thicken the soup later, so don’t skip it even if it feels small.

Pour in the chicken broth slowly while stirring, then add the diced potatoes. Bring everything to a gentle boil, then reduce the heat to a simmer. The broth should look slightly cloudy and smell rich and comforting already.

Let the soup simmer uncovered for 15–20 minutes, or until the potatoes are fork-tender. Stir occasionally to make sure nothing sticks. The potatoes should hold their shape but feel soft and creamy inside.

Lower the heat and slowly stir in the milk or cream. If you’re using cheese, add it now and stir until melted. The soup will turn creamy and smooth, with a pale golden color that looks irresistible.

Add smoked paprika, black pepper, and salt to taste. Give the soup one final stir and let it warm through for a few minutes. Finish with fresh parsley or green onions if you like a touch of freshness.