Roll the thawed puff pastry out into a 9- by 12-inch rectangle. Transfer to a sheet pan lined with parchment paper and fold over a ½-inch border on all sides. Bake the puff pastry according to the package.
In a food processor, combine feta, yogurt, lemon zest and garlic. Process until smooth.
Add the sliced snap peas, radish and mint to a small bowl. Drizzle with olive oil. Crack black pepper over the mixture and toss.
Allow the puff pastry to cool. Using a spatula or knife, spread the feta over the puff pastry. Top the pastry with the vegetable mixture. Drizzle with more olive oil and serve.