Stir chicken broth, water, carrots, celery, onion, lentils, garlic, and red wine vinegar together in a large stockpot; bring to a boil, reduce heat to low, and cook at a simmer until the carrots are tender, about 10 minutes.
Stir ham, mustard, salt, and pepper into the soup; continue cooking until the lentils are tender, 20 to 30 minutes more.
Just before serving, sprinkle some grated Parmesan cheese on top.
For added smoky flavor, add 1 to 2 teaspoons paprika.
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