Place lentils in a large pot, and cover with water (enough so that there's at least a full inch or two of water above the lentils). Bring to a boil and reduce to a simmer. Cook for 15 to 20 minutes, or until the lentils are chewable, but still have some firmness to them. Drain them and set aside.
Heat olive oil in a large pot over medium heat. Add the onion and pepper, and cook for 5 to 8 minutes, or until the onion is soft and clear, stirring frequently. Add the garlic, chili, paprika, and mustard, and continue cooking for another minute or two, until the garlic is quite fragrant.
Add the lentils, fire-roasted tomatoes, tomato paste, brown sugar or maple syrup, apple cider vinegar, salt, pepper, and broth. Bring the mixture to a simmer. Add more broth as needed. Simmer until the mixture has thickened to your liking, about 15 to 20 minutes (I like thick sloppy joes, but if you like 'em sloppier, that's fine, too!).
Remove mixture from heat and allow to cool for a few minutes. Divide sloppy joes onto the buns and top with toppings of choice, including some Tabasco or sriracha for heat, if desired. Serve.
Gena Hamshaw is a certified nutritionist, recipe developer, and food blogger. She shares her latest culinary adventures at The Full Helping. She's the author of two cookbooks, Food52 Vegan (2015) and Choosing Raw (2014). She enjoys yoga, sweet potatoes, cashews, and things that are smothered in sauce.