In a large dutch oven, heat the olive oil over medium. Once hot, add celery and onion. Cook until soft, about 10 minutes. Add potatoes and garlic and cook for an additional 5 minutes, giving some color to the potatoes. Slowly add chicken stock and pepper, cooking until the potatoes are soft, approximately 10 minutes.
While the potatoes are cooking, heat a saucepan.
Cook the diced kielbasa until just crispy, about 5 minutes. Kielbasa can be oily, so this will pull that excess oil rather than adding it to the soup. Remove the sausage from the pan, and place on a paper towel.
Reserve the grease and add enough butter to reach 2 tablespoons of fat. Stir in flour and whisk until the roux starts to bubble. Continue to whisk for about 2 minutes over medium heat.
SLOWLY stir in the milk, ⅓ of a cup at a time, whisking the whole time. Once the milk has been incorporated, stir it into the simmered vegetables.
Add freshly shredded cheese (This matters. Pre shredded cheese doesn’t melt as well) and the kielbasa.
Cook over low-medium heat until the cheese has incorporated.
Serve it up with some fresh bread, a salad, and top with parsley if you choose!