Heat the oven to 350°F. Spray a 12-cup muffin pan, preferably nonstick, with nonstick spray. Set aside.
Heat a large skillet over medium-high heat. Spray with nonstick cooking spray. Add the mushrooms and season with salt and pepper; cook until the mushrooms begin to release their liquids, about 3 minutes. Add the frozen chopped spinach and garlic. Stir to combine. Reduce the heat to medium.
Cook, stirring occasionally until the mushrooms are tender and the mixture is dry, 5 to 7 minutes. Divide the mushroom spinach mixture equally between the 12 muffin tin cups. (There’s no need to pack it down; leave it rough and shaggy.)
One a time, crack 1 egg into the center of each muffin cup. Using the tip of a toothpick, insert the point into the white of each egg and wiggle it slightly so some of the egg white reaches the bottom of the muffin cup. (This helps ensure the cups will remain intact once removed from the tin.)
Transfer to the oven and bake until the whites are set and the yolks are still loose, 10 to 12 minutes. (There will be varying degrees of doneness depending on where they are in the oven, which conveniently creates a selection of soft, medium, or hard-cooked eggs for guests.)
Transfer to a warmed serving platter. Garnish with red pepper flakes and Parmesan cheese. Serve immediately.