Add the sliced red onion, apple cider vinegar, sugar, and a pinch of salt to a small bowl. Stir well and set aside to marinate while you prepare the rest of the recipe.
Add the jarred roasted red peppers, mayonnaise, smoked paprika, lemon juice, and a pinch of salt to a food processor or blender. Blend until completely smooth. Set aside.
Heat the oil in a large skillet over medium heat. Add the chopped onion and minced garlic. Cook for 3 to 4 minutes, stirring occasionally, until soft and fragrant.
Add the ground beef to the skillet and break it up with a spoon. Cook for 5 to 7 minutes until fully browned.
Stir in the Dijon mustard, tomato paste, smoked paprika, and the smoky roasted red pepper sauce until everything is well combined.
Pour in the vegetable broth and stir. Let the mixture simmer for 8 to 10 minutes until it thickens up nicely. Season with salt and pepper to taste.
Spoon generous portions of the sloppy joe filling onto the bottom buns.
Add a slice of cheese on top of the filling, then layer on the lettuce and pickled red onion.
Place the top buns on and serve right away.