Thaw the puff pastry and the frozen spinach according to package directions. Preheat the oven to 425°F. Line two baking sheets with parchment paper.
Heat the butter in a medium sized skillet over medium heat and sauté the onions for 4 minutes until golden brown, then add the spinach and sauté for another 4 minutes or so until cooked and the moisture is gone. Allow to cool to room temperature.
While the spinach mixture is cooling, on a lightly floured surface, lay out one sheet of the pastry, sprinkle lightly with flour and lightly roll it just a little thinner, preserving the shape of the dough. Use a sharp knife to cut it into two even pieces, transfer the pieces to the prepared baking sheets, then use the same knife to score a ½-inch border around the edges, making sure not to cut all the way through the pastry. Use a fork to prick holes in the middle part of the pastry, within the border. Repeat with the other sheet of puff pastry, so you end up with 4 scored pieces of pastry.
Bake the puff pastry for about 10 to 11 minutes until lightly browned and slightly puffy. Remove from the oven, and press within the border lightly with a fork to deflate any puffed up areas, then spread the spinach evenly over the four pieces, keeping the border clear. Sprinkle the spinach with the cheese. Use a spoon to make a little hollow in the spinach and cheese mixture on both ends of all four of the rectangles. Carefully crack an egg into the depressions in the spinach mixture. Repeat until all four pastries have two eggs each. Sprinkle over the bacon, and return to the oven.
Bake for another 8 to 10 minutes until the pastry is fully cooked and the egg is done to your liking. Serve immediately, with chives sprinkled on top if desired.