Preheat oven to 400°F. Line baking sheet with parchment paper or aluminum foil.
Remove stems from mushrooms and place caps open end up on baking sheet. Brush with Calabrian Pesto Olive Oil and season with salt.
Finely chop mushroom stems and set aside to mix into stuffing. In large mixing bowl, combine cream cheese, crab meat, garlic, paprika, ground black pepper, mushroom stems, Basil Olive Oil, salt, and breadcrumbs. Mix well making sure there are no lumps in cream cheese. Stuff mushroom caps with filling, then sprinkle with Parmesan cheese.
Bake uncovered until mushrooms are very tender and filling is nicely browned, about 30 minutes. Serve hot, topped with parsley.