Preheat the oven to 400°F.
Finely dice the onion and bacon, then caramelize them in a little olive oil until bacon is slightly crisp and onion has softened. Drain and set the mixture aside.
Slice the potato, being sure to cut wafer-thin slices to ensure they cook properly in the oven.
Roll the puff pastry out to a rectangle, approximately 12x18 inches, and cut into four equal rectangles, then cut a border of about ½-inch all the way around the rectangle.
Place the tarts on a baking sheet lined with parchment paper. Be sure to leave a bit of space between them because they will puff up and spread as they bake.
Brush each tart with the beaten eggs.
Assemble the Tater Tarts: Lay a few slices of potato down and sprinkle some of the chopped onion and bacon onto the pastry, avoiding the border you just cut. Carefully crack an egg into the center of each tart.
Place the tarts in the oven and bake for about 10 to 15 minutes, or until the pastry is golden and the egg whites have set.
Remove tarts from the oven and garnish with chopped spinach and a sprinkling of salt and a sprinkling of salt and pepper before serving.