In a medium pot, combine the rinsed lentils and vegetable broth. Bring to a boil, then reduce heat to low and simmer for about 20-25 minutes, or until lentils are tender but not mushy. Drain any excess liquid and set aside.
In a large skillet, heat the olive oil over medium heat. Add the diced onion and sauté for 2-3 minutes until translucent.
Add garlic, bell pepper, and grated carrot to the skillet, cooking for another 3-4 minutes until softened.
Stir in the cooked lentils, tomato sauce, tomato paste, maple syrup, apple cider vinegar, Worcestershire sauce, smoked paprika, chili powder, salt, and pepper. Mix well to combine.
Reduce heat to low and let the mixture simmer for an additional 10-15 minutes, stirring occasionally. Adjust seasoning if necessary.
While the filling simmers, toast the whole grain burger buns lightly under the broiler or in a toaster.
Once the filling is ready, scoop a generous amount onto each toasted bun, top with chopped parsley, and serve.