Preheat the oven to 400 degrees F. Line a baking sheet with foil or parchment paper (grease lightly if using foil).
Place the spinach in a bowl with a few tablespoons of water and cover with plastic wrap. Steam in the microwave for 2 minutes, until wilted. (You can also steam the spinach on the stove if you prefer.) Drain extra water and set aside to cool.
Arrange the mushrooms cavity side up on the baking sheet in a single layer. Drizzle with olive oil. Season with sea salt and black pepper.
When the spinach is cool enough to handle, squeeze it tightly several times to drain as much moisture as possible. It should turn into a small, tight ball.
In a medium bowl, mix the spinach, feta cheese, garlic, and parsley. Add sea salt and black pepper to taste if desired. Spoon the mixture into the mushrooms.
Bake for about 15-20 minutes, until the mushrooms are soft and golden.