In a large saucepan, heat the olive oil over medium heat. Add the shallot and green pepper. Cook for 4 to 5 minutes, or until soft. Add the garlic and cook for 1 minute, or until fragrant.
Add the vegetable broth, tomatoes, tomato sauce, mustard, Worcestershire, vinegar, agave, chili, paprika, and salt and pepper. Add the lentils and stir to combine.
Bring to a boil, then reduce the heat to medium-low. Simmer for 30 minutes, or until the lentils are tender and the sauce is thickened.
Divide the lentil mixture between the hamburger buns. Top with desired toppings, if using, and serve.