Preheat oven to 300F and line a sheet pan with parchment paper.
Heat 2 Tbsp oil in a large skillet over medium-high heat.
Add sliced bell peppers and onions, season with salt and pepper.
Sauté 8-10 minutes, stirring often, until softened and caramelized.
Transfer vegetables to a bowl.
Add 2 Tbsp butter to the hot skillet and add shaved steak.
Break steak into bite-sized pieces as it cooks for 4-5 minutes until browned.
Stir in garlic powder, Worcestershire sauce, salt, and pepper.
Reduce heat to medium-low and add vegetables back to pan.
Add half the cheese and stir until melted and combined.
Cut both packages of Hawaiian rolls in half horizontally, keeping halves intact.
Spread 1/4 cup mayo on each cut surface.
Spread steak filling evenly over bottom halves and layer remaining cheese on top.
Place top halves over filling to sandwich.
Melt remaining 1 Tbsp butter and mix in parsley and a pinch of salt.
Brush parsley butter over the tops of both roll sets.
Bake 12-15 minutes until filling is warm and tops are golden-brown.
Slice into individual sliders using roll perforations and serve immediately.