Preheat oven to 425°F/218°C and line a large baking sheet with parchment paper.
Lightly roll the puff pastry to 10-inch (25 cm) square. Cut into 4 squares (a pizza cutter makes this really easy).
Place the pastry squares on the prepared baking sheet and use a sharp knife to score a 1/4-inch (1/2 cm) border around the edge, do not cut all the way through. Use a fork to poke holes all over the inside of the square that you scored. Brush the beaten egg around the edge. Bake for 5 minutes, then remove from the oven. If the centers are puff up, poke with a fork to deflate and if needed, use a sharp knife to re-score.
Sprinkle the cheese over the center of the tarts, arrange the tomato slices, bacon (keeping a small area in the center for the egg) sprinkle some chopped chives. Crack an egg into a small bowl and carefully place in the center of each. Top with more chives and a light sprinkle of salt and pepper. Return back to the oven and bake for 10 more minutes until the egg whites are set, but the yolks still jiggly.