Heat oven to 400°F. Line two baking sheets with parchment.
Stir together beaten egg and water to make an egg wash. Set aside.
Unfold puff pastry on a lightly floured surface. Roll each sheet into a smooth rectangle about 1/8 inch thick.
Spread a thin layer of Dijon over each sheet, leaving a small border. Layer ham evenly, then scatter cheese. Season with pepper and a pinch of salt if using.
Roll each sheet up tightly from a long side to form two logs. Chill the logs in the freezer for 8–10 minutes to firm.
Slice each log into 1/2-inch rounds. Arrange cut-side down on the prepared sheets, spacing slightly.
Brush tops with egg wash and sprinkle with poppy seeds if using.
Bake 16–20 minutes, until puffed and deep golden. Cool 5 minutes, then garnish with chives and serve warm.