Start by preheating your oven to 425°F so it's fully hot by the time you're ready to bake. Unroll your sheet of puff pastry on a lightly floured surface and slice it into 6 even squares or rectangles. Move each piece onto a parchment-lined baking sheet, leaving a little space between them.
Using a sharp knife, score a border about an inch in from the edge of each pastry square, being careful not to cut all the way through. Then use a fork to dock the center repeatedly, which stops that inner section from puffing up too much in the oven.
Whisk one egg with a small splash of water in a bowl to make your egg wash. Brush it generously along the scored border of each pastry piece, which is what gives you that deep golden color once baked. If you like, sprinkle everything bagel seasoning right on top of the wet border now.
Slide the tray into the oven and pre-bake for about 10 minutes. This partial bake is what allows the pastry to actually cook through underneath the egg later, instead of staying raw in the middle. Once it's out, gently press down the center of each square with the back of a spoon to create a little well.
Carefully crack one egg into the center of each deflated pastry square, taking your time so the yolk stays intact. Sprinkle shredded cheese over each egg, then season with a little salt and pepper. Try not to overfill, since the egg white can spread if you're not careful.
Return the tray to the oven for another 10 minutes for a soft, jammy yolk, or a couple minutes longer if you prefer it more set. Keep an eye on it toward the end since ovens vary and you don't want to overcook the yolk by accident.
Once out of the oven, scatter the crumbled bacon and chopped chives generously over each tart. Let them cool for a minute or two before serving, since the cheese and yolk are quite hot straight out of the oven.