Prep the pastry: Unfold your puff pastry sheet on a lightly floured surface. Using a sharp knife, trim it into a 10-by-14-inch rectangle if needed—the dough will shrink as you work.
First butter layer: Brush half of the melted butter evenly over the entire surface. Sprinkle one-third of the shredded cheddar and all the thyme over top, spreading them out but not quite to the edges.
First fold: Fold each long side toward the center so they meet in the middle with a small gap between them (about ½ inch). Brush those exposed surfaces with another thin layer of butter.
Second fold: Now fold the two halves together like closing a book, pressing gently to seal. You should have a thick rectangle about 5-by-10 inches at this point.
Rest and chill: Wrap in plastic wrap and refrigerate for at least 30 minutes while you prep your apples. This keeps the butter from melting into the dough before it hits the oven.
Slice: Preheat oven to 425°F with a rack positioned in the center. Cut the chilled block crosswise into slices about ¾-inch thick.
Arrange and top: Place slices on a parchment-lined baking sheet, leaving at least 1 inch between each (they'll spread). Lay three apple slices across the top of each palmier, press them gently so they adhere to the cheese layer underneath. Sprinkle with remaining cheddar, black pepper, and a light dusting of flaky salt.
Bake: Bake for 18-20 minutes until puffed and golden brown around the edges. The top should be deep amber—don't pull them out too early or they'll deflate.
Cool slightly: Let rest on the baking sheet for 5 minutes before serving. They'll continue to set as they cool.
