Preheat the oven to 350 degrees.

In a large skillet, heat the oil over medium heat. Add the onions and peppers and saute until just starting to soften, about 2 minutes. Push the veggies over to the side and add the ground beef, breaking it into chunks spread evenly across the pan. Cook, undisturbed, for a few minutes until the beef starts to brown. Break the beef into smaller pieces and continue to cook the beef and veggies together, stirring occasionally, until no pink remains. Season to taste with salt and pepper. Drain off any excess fat.

Add the brown sugar, mustard, ketchup, Worcestershire, and apple cider vinegar to the pan. Stir well to coat the beef. Cook for another 2-4 minutes, or until sugar is dissolved and the mixture is well combined.

Line a medium size sheet pan with foil and spray it with cooking spray. Top with the slider buns. Spread the sloppy joe evenly over the bottom half of the sliders. Top with shredded cheese and the top bun.

Whisk together butter and garlic, then brush it over the buns. Sprinkle with Parmesan cheese. Cover loosely with foil and bake at 350 degrees for 10 minutes. Uncover the sliders, then bake an additional 2-3 minutes, or until golden brown. Serve immediately.