Heat the olive oil in a large pot over medium-high heat. Add the sliced kielbasa and cook until browned on both sides, about 5-7 minutes. Remove the kielbasa with a slotted spoon and set aside.
Pour in the chicken or vegetable broth and add the diced potatoes to the pot. Stir in the dried thyme, paprika, salt, pepper, and bay leaf. Bring the mixture to a boil, then reduce the heat to low and simmer for about 15-20 minutes, or until the potatoes are tender.
Return Kielbasa to Pot:
Add the browned kielbasa back to the pot. If using, add the chopped kale or spinach. Continue to simmer for another 5-10 minutes, until the greens are wilted and the kielbasa is heated through.
Add Cream (Optional):
If desired, stir in the heavy cream or half-and-half during the last few minutes of cooking for a richer, creamier soup.
Serve:
Taste and adjust seasoning with additional salt and pepper if needed. Remove the bay leaf before serving. Ladle the soup into bowls and enjoy warm.