Preheat the oven to 400F. Spray a baking sheet with oil.
Gently remove the stems, scoop out the gills and spray the tops of the mushrooms with oil, season with 1/8 tsp salt and fresh pepper.
Season steak with salt and pepper on both sides.
Spray a large skillet with cooking spray and heat on high, let the pan get very hot then add the steak and cook on high heat about 1 to 1 1/2 minutes on each side, until cooked through.
Transfer to a cutting board and slice thin, set aside.
Reduce the heat to medium-low, spray with more oil and saute onions and peppers 5 to 6 minutes, until soft.
Combine all the ingredients in a medium bowl. Transfer to the mushroom caps, about 1/2 cup each.
Bake in the oven until the cheese is melted and the mushrooms are tender, about 20 minutes.