Preheat oven to 400 degrees Fahrenheit (200 degrees Celsius).
Using a rolling pin to roll out 1 sheet puff pasty to about 12 inches (30.5 centimeters) square on a sheet of parchment paper.
Place a 12-inch (30.5 centimeter) plate on puff pastry, then use a sharp knife to cut around plate. Discard excess pastry (or use for something else).
Spread puff pastry circle with pesto, leaving a 1-inch (2.5 centimeter) border.
Sprinkle goat cheese over pesto.
Whisk together egg yolk and 1 tablespoon water. Brush edges of pastry lightly with egg wash (reserve the rest for step #12).
Cut out another puff pastry circle, using same method as in steps 1 and 2. Place over pesto-topped circle, gently pressing out any air pockets.
Place a small glass (or other round object) in center of pastry. Using a sharp knife, cut pastry in quarters, leaving center intact.
Cut each quarter in half (you should have 8 sections when done).
Cut each of the eight sections into 4 more sections (you should have 32 sections when done).
Twist each section 3-4 times, placing ends flat on on parchment paper. Carefully slide parchment paper / tarte onto pizza pan (or baking sheet) when finished twisting.
Brush tarte with egg wash, then sprinkle with sesame seeds.
Bake for 20 to 25 minutes, or until puffy and deep golden brown.
Serve tarte hot, warm, or at room temperature. Enjoy!
Notes
Puff Pastry Tips - Thaw puff pastry in you refrigerator overnight, then keep the pastry in your refrigerator until you're ready to roll it out. Work with one sheet at a time, and work as quickly as possible, so the pastry stays cool. You can also refrigerate or freeze the pastry before baking, and this will actually help it puff up more.Size - Tarte can be made anywhere from 10 to 12 inches square (25.4 to 30.5 centimeters), depending on the size of your plate. Other round objects, such as platters, baking pans, etc., can also be used to create the circle. I used the lid from a cake keeper.Step-by-StepPhotos - Make sure to read the info before this recipe card for step-by-step photos, helpful tips, alternate filling ideas, related recipes, and more!