Rinse lentils. In a medium saucepan, add the lentils and the 1 cup water and 1 cup vegetable broth. Bring to a low boil and then cook, uncovered, for 18 minutes or until tender. Drain excess liquid when done. (Add more liquid if they aren’t tender and are looking dry, which is unlikely.)
While that cooks, peel and trim the onion and cut out the middle third, for rings to top the sandwiches. Take the other two thirds and chop finely, adding to a bowl, along with 3 cloves garlic (minced), 1-2 green bell peppers (chopped) and the jalapeno (finely chopped).
Heat butter and olive oil (2 tbsp total) in a skillet on medium-high. Add the onions and peppers and cook until they are fragrant and starting to brown. Then, add the tomato sauce or passata, the 1 tsp sugar, 2 tbsp Worcestershire sauce, 2 tsp ground cumin, 1 tbsp smoked paprika, 1 tsp dry mustard and 1 tsp oregano. Add salt to taste.
When the lentils are done (and drained), add them to the mix and continue cooking over medium-low heat until cooked through and fairly thick. Taste and adjust flavoring as needed.
Serve on toasted buns with rings of white onion.