Turn the oven to broil. Clean mushroom caps and, if desired, lightly scrape the gills out of the underneath of each cap. Brush mushrooms on both sides with olive oil , and season with salt and pepper. Place gill side down on a sheet pan and cook for about 3-5 minutes. Remove from the oven.
Turn the oven down to 350°F.
Turn the mushrooms gill side up and start building. First, place the spinach into the cap building up the sides and creating a well in the middle, if necessary, to accommodate the egg. Add some goat cheese and Carefully break one egg into the well of each of the mushroom caps.
Now place them back into your 350°F oven and bake for 15 to 17 minutes depending on how well done or sunny-side-up you like your eggs. Serve immediately.