Preheat oven to 375°F (190°C) and line a baking sheet with parchment.
Clean mushroom caps, remove stems, and pat them dry.
Lightly brush caps with olive oil and arrange top-side down on the prepared sheet.
In a bowl, combine softened cream cheese, mayonnaise, Dijon mustard, lemon juice and Worcestershire until smooth.
Fold in crab meat, diced red pepper, scallions, parsley, Parmesan, Old Bay, salt and pepper; taste and adjust seasoning.
Fill each mushroom cap generously with the crab mixture, mounding slightly.
Mix toasted panko with a little extra grated Parmesan and sprinkle over each filled cap.
Bake for 18–22 minutes until filling is set and tops are golden brown.
Remove from oven and let cool slightly to set.
Garnish with extra parsley or lemon zest and serve warm.