In a large pot, heat olive oil over medium heat. Add sliced kielbasa and cook until browned. Remove and set aside.
In the same pot, add chopped onion and cook until softened, about 3-4 minutes. Add minced garlic and cook until fragrant, about 1 minute.
Pour in chicken broth. Add cubed potatoes, sliced carrots, and chopped celery. Stir in dried thyme and parsley. Season with salt and pepper.
Bring to a boil, then reduce heat and simmer until potatoes and carrots are tender, about 20 minutes.
Stir in heavy cream and return kielbasa to the pot. Simmer for an additional 5 minutes, until heated through.
