Preheat broiler, setting the temperature to high. Set an oven rack in the middle of the oven (you don't want the mushrooms too close to the heating element for this recipe). Line a broiler-safe rimmed baking sheet with foil.
Wipe the mushrooms clean with a damp paper towel. Gently twist off or the stem of each mushroom. Holding each mushroom in one hand, use a spoon to gently scrape out the gills.
Spray the mushroom caps with olive oil cooking spray on both sides. Sprinkle with ½ teaspoon kosher salt and ⅛ teaspoon black pepper. Broil 5 minutes on each side, or until just tender.
Meanwhile, defrost the spinach in the microwave according to the directions on the package (my package said to cut a small slit in the wrapper, place on a microwave-safe plate and microwave for 4-6 minutes). Place in a colander to drain. When cool enough to handle, press on the cooked spinach with your hands and extract as much water as possible out of it. Repeat this until you're sure you can no longer extract more water.
Remove the mushrooms from oven. Heat 1 tablespoon olive oil in a large skillet over medium heat, about 3 minutes. Add the onion and cook 5-7 minutes, stirring occasionally, until golden. Add the garlic, spinach, ½ teaspoon kosher salt and ⅛ teaspoon black pepper and cook, stirring to combine everything, 1-2 more minutes. Remove from heat and allow to cool a few minutes, then mix in the Parmesan.
Evenly distribute the spinach mixture among the mushrooms. Don't press down on the filling - it's prettier when it's piled high on top of the mushrooms. Place back under the broiler for 2-3 minutes, or until filling is golden.