In a large soup pot, heat the oil over high heat. Reduce the heat to medium-high, add the carrot, celery and onion and saute for 5 minutes. Add the garlic and saute for another 1 to 2 minutes.
Add the cabbage to the pot and cook, covered, stirring regularly to prevent burning, until softened, 6 to 8 minutes. Add the kielbasa and mustard and then add the chicken broth. Bring to a simmer and cook until the carrots are tender, 15 to 20 minutes.
In a bowl, mix together the butter and flour to form a buerre manier. Whisk the buerre manier into the soup and simmer for 20 minutes. Season with salt and pepper.