Preheat the oven to 375 degrees F. Line a large baking sheet with parchment paper or foil.
Rinse mushrooms and gently pat dry. Remove stems and gills to create an open cavity for steak mixture. Place on prepared baking sheet, stem side up. Place one piece of provolone cheese inside of each portobello cap.
In a large skillet set to medium-high, melt 2 Tbsp. butter. Once melted, add minced garlic. Let cook for 1-2 minutes, until fragrant. Add chopped bell peppers, onion, 1 Tbsp. Worcestershire sauce, and ground paprika. Add salt and pepper, to taste. Let cook for 7-10 minutes until veggies are tender, stirring occasionally.
Move veggies to the outer rim of the pan. Add remaining 2 Tbsp. butter. Once melted, add shaved steak and remaining 1 Tbsp. Worcestershire sauce. Cook for 3-5 minutes to lightly brown the meat.
Mix meat and pepper-onion mixture together, cook an additional 3 minutes.
Divide meat and veggie mixture between each mushroom cap (about 1/4 cup of mixture in each). Place a provolone cheese slice on top of each.
Bake for 15-20 minutes, or until cheese is melted and mushrooms are tender.