Step 1

Preheat the oven to 400°F. Arrange the oven racks to the upper and lower thirds of the oven. Line two baking sheets with parchment paper.

Step 2

In a medium bowl, combine the oil, vinegar, honey, salt, and pepper. Add the radishes and toss to coat.

Step 3

Cut a sheet of puff pastry along the folds to form 3 long columns. Cut each column in half crosswise to form 6 (4-by-3-inch) rectangles. Repeat with the remaining sheet of puff pastry. Divide the cheese among all 12 rectangles, spreading evenly, with a ½-inch border on all sides.

Step 4

On the prepared sheet of parchment, shingle 16 radish slices into a (3-by-2-inch) rectangle so that it will be covered by the puff pastry, reserving any remaining vinegar mixture. There should be 6 arrangements on each sheet pan. Place the puff pastry sheets cheese-side down on top of the radishes. Use a fork to crimp the edges of the pastry down over the radishes. Brush the surface with the beaten egg.

Step 5

Bake until the puff pastry is golden brown, 25 to 30 minutes, moving the pan on the top rack to the bottom, and the pan on the bottom rack to the top after 20 minutes.. Allow the pastry to cool for 5 minutes before gently flipping them over and moving them to a wire rack. Enjoy warm or at room temperature, with an extra drizzle of the reserved vinegar mixture and a sprinkle of chives.