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Cook Sausage: In a large pot, heat olive oil over medium heat. Add sliced kielbasa and cook until browned. Remove and set aside.
Sauté Vegetables: 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.
Add Broth and Veggies: Pour in chicken broth.
Add cubed potatoes, sliced carrots, and chopped celery. Stir in dried thyme and parsley. Season with salt and pepper.
Simmer: Bring to a boil, then reduce heat and simmer until potatoes and carrots are tender, about 20 minutes.
Finish Soup: Stir in heavy cream and return kielbasa to the pot. Simmer for an additional 5 minutes, until heated through.