Lay a large piece of plastic wrap on work surface. Unroll the first sheet of puff pastry in the center of the plastic. Spread with half of the mustard, leaving a 1/2-inch border on all sides. Lay 6 ham slices on top, overlapping as needed. Sprinkle with half each of the cheese and thyme.

Re-roll puff pastry into a log, pinching seam to seal. Wrap in plastic wrap. Repeat with remaining pastry mustard, ham, cheese and thyme. Refrigerate logs until cold, about 20 minutes.

Meanwhile, preheat oven to 400°F; line two rimmed baking sheets with parchment paper.

Using a serrated knife, cut each log into 12 slices. Arrange the rolls, cut-side down, 1 inch apart on the prepared baking sheets. Bake until the puff pastry is light golden brown and the cheese is hot and bubbly, 18 to 22 minutes; let cool slightly on rack.

Serve warm or at room temperature. Garnish with chives.

Tips: Pinwheel logs can be made and refrigerated a day ahead; slice and bake as directed when ready to serve.