Rinse and drain the lentils. In a large pot, combine the lentils, vegetable broth, onion, garlic, smoked paprika, chili powder, cumin, and cayenne pepper. Bring to a boil over high heat.
Reduce heat to low and simmer for 25 minutes or until lentils are tender. Stir in tomato paste, brown sugar (or maple syrup), and apple cider vinegar. Simmer for an additional 5 minutes.
Season with salt and pepper to taste. Serve on hamburger buns or over cooked rice.