Divide the bacon slices among 2 large skillets. Cook in a single layer over medium-low heat, flipping once and draining the rendered fat as needed, until the bacon is almost fully cooked but still pliable enough to bend, 5 to 7 minutes. Drain the bacon on a paper towel-lined plate and set aside.
Unfold the puff pastry sheets onto a lightly floured work surface. Lightly roll each sheet with a rolling pin to seal together any folds..
Using a sharp knife, cut each sheet into 9 equal squares. Place 1 puff pastry square in each cup of a 12-cup muffin pan, pressing it firmly into the bottom and sides and letting the edges hang over the cup. (Reserve and freeze the 6 leftover squares for another use.)
Place 1 of the bacon strips in each puff pastry cup, letting the ends stick out.
In a large bowl, whisk together the eggs with the milk and a pinch each of salt and pepper.
Divide the cheese among the puff pastry cups, followed by the egg mixture.
Bake until the puff pastry is golden brown and the eggs are cooked through, 18 to 22 minutes. Let cool in the pan for 5 minutes then loosen the pastry cups around the edges with a paring or butter knife.
Sprinkle the egg cups with the chives and serve immediately.