Preheat the oven to 400 degrees F. Line a sheet pan with parchment paper.
Add the butter to a nonstick skillet over medium heat. Beat 6 of the eggs together in a bowl. When the butter has melted, add the beaten eggs and the chives to the skillet, then a pinch of salt and pepper. Scramble the eggs until cooked through, about 2 minutes. Remove from the heat and add to a bowl to cool slightly.
Add the ham, mozzarella and Cheddar to the eggs and mix to combine. Set aside.
Make an egg wash with the remaining egg and a splash of cold water in a small bowl.
Lay out the sheets of puff pastry and cut into twelve 3-by-5-inch rectangles. Divide the egg mix among six of the puff pastry rectangles, leaving borders empty around the edges. Brush the borders with the egg wash and top each with another puff pastry rectangle. Using a fork, crimp the edges to seal. Transfer to the lined baking sheet. Brush the tops with the egg wash and sprinkle with the poppy seeds. Bake until golden, about 20 minutes.