Heat olive oil in a large pot over medium heat, add sliced kielbasa, and cook for 5–7 minutes until golden brown. Remove kielbasa and set aside.

In the same pot, sauté chopped onion and celery for 4–5 minutes, then add minced garlic and thyme, cooking for an additional 30 seconds.

Pour in chicken stock, add cubed Yukon Gold potatoes, and half of the sautéed kielbasa back into the pot. Simmer for 20 minutes.

Remove half of the soup and blend until smooth, then return to the pot. Stir in cream and grated cheese until melted.

Ladle into bowls, garnish with green onions and extra cheese, and serve hot.