Cook the Lentils: Place the rinsed lentils, 3 cups water, and salt in a 3-quart (2.8-liter) saucepan. Bring to a boil over medium-high heat, then reduce the heat to maintain a gentle simmer. Cook uncovered for 20 to 25 minutes, stirring occasionally, until the lentils are tender but still hold their shape.

Drain the Lentils: Pour the cooked lentils into a fine-mesh sieve or colander and drain thoroughly. Let them stand while the sauce is prepared. You should have about 2 1/2 cups of cooked lentils.

Soften the Vegetables: Heat the olive oil in a 12-inch (30 cm) deep skillet over medium heat. Add the onion and green bell pepper. Cook for 6 to 8 minutes, stirring occasionally, until the onion is translucent and the pepper is tender.

Add the Garlic and Tomato Paste: Stir in the garlic and cook for 30 seconds. Add the tomato paste and cook for 1 to 2 minutes, stirring constantly, until it darkens slightly and begins sticking lightly to the skillet.

Build the Sauce: Add the tomato sauce, ketchup, maple syrup, yellow mustard, apple cider vinegar, soy sauce, smoked paprika, chili powder, black pepper, and 1/3 cup water. Stir until smooth and bring the mixture to a gentle simmer.

Simmer the Sauce: Reduce the heat to medium-low and cook uncovered for 5 minutes, stirring occasionally. The sauce should look glossy and slightly thickened, without tasting sharply of raw tomato paste.

Add the Lentils: Stir the drained lentils into the sauce until evenly coated. For a more cohesive sloppy joe texture, lightly mash about one-quarter of the lentils with a potato masher or the back of the spoon, leaving most of them whole.

Thicken the Filling: Simmer uncovered for 6 to 10 minutes, stirring frequently, until the filling is thick enough to mound on a spoon. If it becomes too thick before the flavors blend, add water 1 tablespoon at a time. If it looks watery, continue simmering uncovered.

Rest the Filling: Remove the skillet from the heat and let the filling stand for 5 minutes. It should thicken slightly and remain moist without releasing liquid around the edges.

Assemble the Sandwiches: Spoon about 3/4 cup of lentil filling onto each toasted bottom bun. Add sliced dill pickles, if using, and close with the top buns. Serve immediately.