Preheat the oven to 425 degrees . On a rimmed baking sheet, brush the mushrooms with EVOO and season with salt and pepper; situate them rounded side up. Roast until softened, 8 to 10 minutes.
Meanwhile, in a large skillet, heat 2 tbsp. EVOO, 2 turns of the pan, over medium-high heat. Pat the beef dry and add to the skillet; season with salt and pepper. Cook, stirring, until browned, about 5 minutes. Add the onion, garlic, worcestershire and marjoram (or oregano). Cook until the onion and garlic are softened, about 5 minutes. Add the watercress to wilt. Stir in the panko. Remove the pan from the heat; stir in the pecorino-romano.
Flip the mushroom caps over so theyre rounded side down and fill with the meat mixture, mounding a quarter of the beef into each cap. Top with the provolone and return to the oven to melt the cheese, 7 to 8 minutes.