Preheat the broiler, setting the temperature to high. Set an oven rack in the middle of the oven. Line a rimmed, broiler-safe baking sheet with foil.
Wipe the mushrooms clean with a damp paper towel. Gently twist off or cut the stem of each mushroom. Holding each mushroom in one hand, use a spoon to gently scrape off the gills.
Spray the mushrooms with olive oil on both sides. Sprinkle them with ¼ teaspoon kosher salt, ⅛ teaspoon pepper, and ¼ teaspoon garlic powder. Broil in the middle of the oven until just tender, about 5 minutes on each side.
Remove the mushrooms from the oven. Drain any liquids. Switch the oven from broil to bake, setting the temperature to 400°F.
Break an egg into each mushroom. If your eggs are large, you'll need to break each egg into a small bowl and pour some of the egg white out before pouring the egg into the mushrooms.
Sprinkle the mushrooms with the cheese. Bake until the egg whites are cooked, about 15 minutes.
Sprinkle the eggs with the remaining ¼ teaspoon of salt and ⅛ teaspoon of black pepper. Garnish with parsley and serve.
During the final step of baking, bake just until the egg whites are cooked. Baking too long will result in mushy mushrooms that have released their liquid into the eggs. But even if that happens, do not despair: carefully drain the liquid and place the mushrooms on paper towels to soak as much of the liquid as you can.
The mushrooms are the stars of the show, so choose them well. It's best to use large, firm portobello mushrooms. You don't want them too flat (or the egg will spill) or too deep (or the egg will take forever to cook).
These mushrooms are best enjoyed right away. If you must keep leftovers, do so only if the eggs are fully cooked. Place the leftovers on paper towels in an airtight container (to absorb extra liquid) and keep them in the fridge for up to 3 days. Replace the paper towels daily. Reheat them in the microwave, covered, at 50% power. I don't recommend freezing the leftovers.