Preheat the broiler, setting the temperature on high. Set an oven rack in the middle of the oven (this will prevent the mushrooms from scorching under the broiler). Line a broiler-safe rimmed baking sheet with foil.
Spray the mushroom caps with olive oil cooking spray on both sides. Broil in the middle of the oven until just tender, about 5 minutes on each side.
Meanwhile, transfer the crab meat to a medium bowl, feeling through the meat to make sure no shell pieces remain.
Add the remaining ingredients except for the paprika and mix well, with a fork or a spatula, to combine.
If the broiled mushrooms have released water, drain them on paper towels, then stuff them with the crab mixture. Sprinkle with the paprika.
Broil 2-3 minutes, just until the filling is warm and golden. Serve immediately.