Sprinkle flour lightly onto a large cutting board or marble work surface.
Place the puff pastry sheet on top, and use a rolling pin to gently roll out the puff pastry dough to a 10 x14 rectangle. (See note below if using a 2-sheet package)
Spread the puff pastry dough with pesto, then crumble the goat cheese on top.
Working from the long sides, roll up each side until they meet in the middle.
Carefully move the rolled dough onto a parchment-lined cutting board and put into the freezer to chill for 30 minutes.
Preheat oven to 425° F while dough is chilling.
When dough is firm, place on cutting board and cut into slices about ½-inch thick. You will get about 20 slices.
Place the slices carefully on a parchment paper-lined baking sheet, about 2 inches apart. They spread out, so I recommend baking 10-12 at a time.
Bake for 14-16 minutes, until lightly browned on the edges.
Use a spatula to flip them over, then bake another 3-4 minutes, until they are fully browned.
Remove pan from oven. After 2 minutes, use a spatula to transfer palmiers to a cooling rack.
Serve warm, or let them cool completely if you're making them ahead. Repeat with the remaining slices.
Notes
Storage Tips:Store baked palmiers in an airtight container for up to 3 days. Re-warm them on a baking sheet in a 350° F oven for about 5 minutes before serving, if you’d like. You can also freeze baked palmiers in a freezer safe zip-top bag for up to 3 months. Defrost at room temperature, and warm them up if desired.Expert Tips:I use Dufour pastry dough with this recipe. If you use a box of puff pastry dough that comes with 2 sheets, such as Pepperidge Farm, you won’t be able to roll it out to 10x14. Roll each sheet to 9x12, or just until the puff pastry dough is slightly thinner than how it comes out of the package. You can either make both sheets and freeze any leftovers, or save the 2nd sheet for another purpose.Make sure your dough isn’t sticking to your work surface before you add the pesto and goat cheese. Once the toppings are on, it's difficult to roll the dough without stretching it if the dough is sticking to the work surface. Move the dough around as you are rolling, and use enough flour underneath as you need.Keep the puff pastry dough roll snug, so your palmiers bake into neat, even swirls. If the dough gets too warm and won't roll smoothly, put it in the refrigerator for a few minutes.Don’t skip the step of freezing the log before slicing. Cold dough slices cleanly and puffs up into those tall, flaky layers in the hot oven thanks to the hot oven meeting the cold butter in the dough.