Place a soup pot over medium-high heat with 2 turns of the pan EVOO, about 2 tablespoons. Once hot, add the kielbasa and cook until brown and crispy, about 4-5 minutes. Remove from the pot and reserve on paper towel-lined plate.
To the same pot, add the leeks, thyme, garlic, hot sauce, nutmeg, salt and freshly ground black pepper. Cook, stirring frequently, for 8-10 minutes, until the leeks are tender.