Preheat oven to 350. Rinse mushrooms under cold water to remove any dirt. Remove stems from mushrooms and reserve. Place mushrooms on a baking sheet gill side up and roast for 15 to 20 minutes. Remove from oven, drain any water in mushroom caps, and allow to cool.
Finely dice 1/4 of the reserved mushroom stems. Blend diced mushroom stems, goat cheese, old bay, and crab meat. Add more old bay as needed. Stuff mushrooms with mixture until well rounded. Top with gruyere and bake until heated through and cheese begins to melt. Remove from oven, garnish with scallions, and serve.