Cook the Veggies: In a pan over medium heat, add neutral oil. Once hot, toss in the diced onion and sliced bell pepper. Season with a pinch of salt and black pepper. Sauté until softened and slightly caramelized, about 5 to 7 minutes. Stir in the minced garlic and cook for 1 to 2 minutes until fragrant. Remove from the pan and set aside.
Cook the Steak: In the same pan, melt butter with neutral oil over medium-high heat. Add the shaved steak, breaking it apart as it cooks. Season with salt, paprika, mustard powder, and black pepper. Once the steak is browned, pour in Worcestershire sauce and cook for another minute. Then, pour in the beef broth to deglaze the pan, scraping up any browned bits for extra flavor. Let it simmer for 2 minutes until slightly reduced. Remove from heat.
Prepare the Rolls: Preheat the oven to 350°F (175°C). Keeping the Hawaiian rolls connected, slice them in half horizontally. Spread a thin layer of mayonnaise on the cut sides. Place them mayo-side up on a baking sheet and toast in the oven for a few minutes until lightly golden.
Assemble the Sliders: Place the bottom half of the toasted rolls in a baking dish or tray. Evenly spread the cooked steak over the bread, then layer the sautéed veggies on top. Add your choice of Cooper Sharp, provolone, or Cheese Whiz over the veggies. Place the top half of the rolls on.
Finish and Bake: Brush the tops with melted butter and sprinkle with toasted sesame seeds. Cover loosely with foil and bake for 10 to 15 minutes until the cheese is melted. Then, remove the foil and bake for another 5 minutes until the tops are golden brown.
Serve: Let the sliders cool slightly before pulling them apart. Enjoy warm!