1. Preheat the oven to 400 degrees F. On a lightly floured surface, roll the puff pastry to a 13-inch-by-10-inch rectangle and transfer to a parchment-lined baking sheet. Prick the pastry all over with a fork and scatter with the leeks and both cheeses. Sprinkle with a pinch of kosher salt and 1/4 teaspoon pepper.
2. Bake until the pastry is a deep golden brown and the leeks are tender, 25 to 30 minutes. Cool for 10 minutes. Garnish with the chopped chives, cut into 16 or 24 pieces and serve.