Preheat oven to 400 degrees F (200 degrees C). Line a baking tray with parchment paper and dust lightly with flour.
Lay puff pastry on a flat work surface; cut a 12-inch circle from each sheet. Transfer 1 circle to the prepared baking sheet.
Spread ricotta evenly over the pastry circle. Top with an even layer of pesto. Lay the second pastry circle on top. Set a small glass upside down in the middle of the circle.
Cut the circle, away from the glass, into 4 equal quarters. Cut each quarter in half, then each eighth in half, to make 16 equal strips. Remove glass. Twist strips twice, two at a time, in the opposite direction. Pinch ends together. Repeat with remaining strips to make a pinwheel shape.
Bake in the preheated oven until pastry is browned, 25 to 30 minutes.
If your pesto is particularly oily, which can be the case with some store-bought pesto, strain it through a fine sieve to remove some of the excess oil. Too much oil could result in pastry that is soggy or greasy.
If at any point the pastry becomes too soft, refrigerate it for 20 minutes. Keeping it cool ensures the puff pastry keeps its flaky layers.
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