Heat ½ tbsp (7 mL) of the oil in the 8-qt. (7.6-L) Brilliance Nonstick Stock Pot over medium heat for 2–3 minutes.
Add the sausage. Cook over medium heat for 6–8 minutes, breaking the sausage into crumbles. When the sausage is no longer pink, drain and remove from the pot.
Add the remaining oil, carrots, onion, tomatoes, garlic, and oregano. Cook and stir over medium heat for 4–5 minutes, or until the tomatoes begin to burst.
Add the sausage, stock, and lentils to the pot. Cover and bring to a boil over high heat. Reduce the heat to a simmer and cook, uncovered, for 20 minutes, stirring occasionally.
Stir in the kale and vinegar. Let it stand, uncovered, for 4–5 minutes or until the kale is wilted. Top with Parmesan cheese and serve.