Pre heat oven to 350 degrees.
In a large skillet over medium heat, heat the olive oil and 2 tablespoons of the butter. Add the mushrooms and cook, stirring occasionally, until golden brown. About 5 minutes.
Add the remaining 2 tablespoons of butter along with the shallots, garlic and thyme. Stir and cook until the shallots have softened, about 3 minutes. Add the salt and worcestershire and cook for another 3 minutes or until well combined.
Meanwhile, make the topping for the rolls. Put the butter in a small bowl and microwave until melted. Add the Parmigiano Reggiano, garlic powder and kosher salt. Stir to combine.
Cut the slider rolls in half, separating the top and the bottom. Place the bottoms in a parchment lined baking pan. Layer half of the cheese, then the mushroom mixture, then the other half of the cheese and cover with the top of the rolls.
Brush the tops with the melted butter mixture and bake for 12-15 minutes, until the buns are golden brown and the cheese has melted. Following the lines of the rolls, cut into individual sliders.