Bring a large pot of water to boil. Split fava pods lengthwise and slide your finger along the inside to coax the beans into a bowl. Add beans to boiling water and cook for 2-3 minutes (longer for larger beans); lift out with a slotted spoon into a strainer and rinse to cool. Pierce each fava bean’s outer skin with your thumbnail and transfer inner beans to a small bowl, discarding skin. Set aside.

Arrange squares of puff pastry on prepared baking dish. Bake at 400 degrees for 20 minutes.

While the pastry squares bake, add fava beans, feta, chives, mint, thyme, and lemon zest and juice to the bowl of a food processor; pulse 4 or 5 times until mixture is combined and fava beans are unevenly chopped. Add salt and pepper to taste and pulse once more. (Alternately, you can mix this all together in a medium bowl, using the back of a fork to crush fava beans to your desired size.)

Once the pastry squares have baked for 20 minutes, remove from the oven and spoon ¼ of the fava mixture on top of each pastry square. Return to oven and bake 15 minutes more. Transfer tarts to a platter or individual plates. Serve sprinkled with fresh chive flowers if desired.