In a medium pot, combine red lentils and vegetable broth, bringing to a simmer over medium heat. Cover and reduce to low, cooking for about 10 minutes until lentils are tender.

Dice yellow onion and red pepper, mince garlic, and chop cauliflower. Prepare all vegetables for seamless cooking.

In a mixing bowl, combine tomato sauce, brown sugar, tomato paste, Worcestershire sauce, vinegar, chili powder, cumin, salt, and pepper. Stir until well blended.

Heat a large skillet over medium-high heat; add olive oil. Add onion, garlic, and red pepper; sauté for 2-3 minutes until onion is translucent.

Stir in chopped cauliflower and cook for 2 minutes to soften it slightly.

Add sauce to skillet with sautéed vegetables. Simmer for about 5 minutes; then add cooked lentils and stir, cooking for another 5 minutes until thickened.

Scoop portions of the mixture onto hamburger buns and serve warm.