Cook kielbasa: In a large pot, heat olive oil and cook sliced kielbasa until browned. Remove and set aside.

Sauté veggies: In the same pot, add butter, onions, and garlic. Cook until onions are translucent.

Add potatoes and broth: Stir in potatoes and chicken broth. Bring to a boil, then reduce heat and simmer until potatoes are tender, about 15 minutes.

Thicken soup: In a separate bowl, whisk flour into milk until smooth. Gradually add to the pot, stirring constantly until the soup thickens.

Combine: Return kielbasa to the pot, add shredded cheese, salt, and pepper. Stir until cheese is melted.

Serve: Garnish with fresh parsley before serving.