Wipe the mushrooms with a damp paper towel, twist out the stems, and chop the stems finely (about 1 cup).

Toss the caps with 1 tablespoon olive oil and 1/4 teaspoon salt, set them hollow side down on the sheet, and roast 8 minutes, until the caps look shiny and slightly shrunken with liquid pooled on the parchment.

While the caps roast, melt 1 tablespoon butter in the skillet over medium heat. Cook the chopped stems 5 to 6 minutes, stirring only every 30 seconds, then add the garlic for 30 seconds, until the pan looks dry and the pieces are golden brown.

Move the roasted caps to a plate lined with paper towels and swap the wet parchment for a fresh sheet, until the caps look dry and the sheet looks clean.

Scrape the stems into a large bowl and cool 5 minutes. Add the cream cheese, 1/2 cup Parmesan, 1/4 cup panko, parsley, lemon juice, paprika, 1/4 teaspoon salt, and pepper, and stir until the filling is thick and holds a mound on the spoon.

Set the caps hollow side up on the clean sheet and spoon about 1 heaping tablespoon of filling into each, mounded slightly above the rim, until each cap holds a rounded dome.

Mix 1/4 cup panko, 2 tablespoons Parmesan, and 1 tablespoon melted butter, then press a pinch onto each dome until every dome is covered and the topping looks like damp sand.

Bake on the center rack 15 to 18 minutes, rotating the sheet halfway if your oven runs hot in the back, until the tops are golden brown and the filling bubbles at the edges.

Rest the tray 5 minutes before serving, until the filling firms up and stops sliding when you lift a mushroom.