1Heat the oven to broil and arrange a rack in the middle. Line a large plate with paper towels; set aside.
2Coat a baking sheet with olive oil and place in the oven for 2 minutes. Remove the baking sheet from the oven and evenly arrange mushrooms, cap side down and 1 inch apart, on the baking sheet. Broil until the surface of the caps touching the baking sheet is golden brown, about 4 to 5 minutes. Remove from the oven and transfer mushrooms to the paper-towel-lined plate, browned side up, discarding any moisture collected inside the caps; set aside. Wipe the baking sheet dry with a paper towel; set aside.
3Place panko in a medium frying pan over medium-high heat. Toast, stirring occasionally, until lightly browned, about 5 minutes. Transfer to a medium bowl; set aside. Wipe any crumbs from the pan with a paper towel.
4Reduce heat to medium, return the pan to heat, and melt butter until foaming. Add shallot, paprika, salt, and pepper and sauté, stirring occasionally, until shallot has softened, about 3 minutes. Add sherry and cook until the alcohol smell has dissipated, about 2 minutes. Add toasted panko and stir to combine. Remove mixture to a medium bowl and let cool slightly.
5Meanwhile, transfer mushrooms, cap side down and 1 inch apart, to the dried baking sheet.
6Add crabmeat, cheese, and lemon juice to the reserved shallot mixture and gently fold until evenly incorporated. Divide filling evenly among mushrooms. Broil until the cheese is melted and bubbling, about 3 minutes.