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.
Use damp paper towels to gently wipe the mushrooms clean. Gently twist the stems off. Spray the mushrooms with olive oil on both sides. Broil in the middle of the oven until just tender, 2-3 minutes per side. Drain on paper towels.
Transfer the crabmeat to a medium bowl, feeling through the meat to ensure no shell pieces remain. If using jumbo lump crabmeat (which comes in larger pieces than lump crabmeat), use a fork to break the lumps into smaller pieces.
Add the remaining ingredients except the paprika and mix well with a rubber spatula until thoroughly combined. Taste to ensure the filling is salty enough for your palate. If not, add salt to taste.
Spoon the crab mixture into the mushrooms, dividing it evenly. Each mushroom should hold about 2 tablespoons of filling. Pack the filling into the mushrooms and pile it high if needed. Sprinkle the stuffed mushrooms with paprika.
Arrange the mushrooms, filling side up, back on the baking sheet (you might need to use a clean new sheet of foil). Lightly spray them with olive oil.
Broil the mushrooms briefly, just until the filling is warm and golden, for about 3 minutes. Serve immediately.
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Notes
The fresher the crab meat you use, the better this appetizer will taste. I find that the supermarket lump crabmeat that comes in small plastic containers tends to be quite fishy, so I don't like to use it in this recipe. If you have Whole Foods Market in your area, I suggest you try the crab meat sold at their seafood counter. It's the freshest I have been able to find.
Pick larger mushrooms. If you’re buying pre-packed baskets, you’ll probably need to buy an extra one. Use the smaller mushroom in this sautéed mushrooms recipe or to make cream of mushroom soup.
Crabmeat is very salty, so I find that there's no need to add salt to the mixture. You can, of course, taste the filling and decide for yourself.
You can keep the leftovers in the fridge, in an airtight container, for 3-4 days. Reheat them gently in the microwave at 50% power or in a 350°F oven. They are also good when served cold.