Make sure you have a rack in the bottom level of the oven. Preheat the oven to 400 degrees F. Line a large baking sheet with parchment paper.
Lay a sheet of puff pastry on the prepared baking sheet. Use a 3-inch cutter to cut four circles into the puff pastry (do not remove the circles).
In a small bowl, whisk together one egg, water and mustard. Brush the pastry sheet with the egg wash- brushing around the circles.
Press tomatoes and spinach lightly into the puff pastry, avoiding the circles. Brush again with the egg wash.
Bake the pastry sheet on the bottom rack for 12 minutes. Remove from the oven, cut the circles with the cutter again, remove the circles of pastry and discard. Crack 4 eggs into the four circles open on the pastry.
Return to the oven and bake 4 to 5 minutes, or until the eggs are cooked as you like them. Sprinkle with Parmesan cheese, salt and pepper. Use a pizza cutter to cut into four slices, and serve immediately.