Lightly flour a board and carefully unfold one sheet of puff pastry. Roll the pastry lightly with a rolling pin until it's 9 1/2 by 11 1/2-inches. Spread the sheet of puff pastry with half the pesto, then sprinkle with half the goat cheese, half the sundried tomatoes, and half the pine nuts. Sprinkle with 1/4 teaspoon salt.
Working from the short ends, fold each end halfway to the center. Then fold each side again towards the center until the folded edges almost touch. Fold one side over the other and press lightly. Place on a baking sheet lined with parchment paper. Repeat the entire instructions for the second sheet of puff pastry using the remaining ingredients. Cover with plastic wrap and chill for at least 45 minutes.
Meanwhile, preheat the oven to 400 degrees F.
Cut the prepared rolls of puff pastry in 1/4 inch thick slices and place them face up 2 inches apart on baking sheets lined with parchment paper. Bake for 14 minutes, until golden brown. Serve warm.
Place the walnuts, pignolis, and garlic in the bowl of a food processor fitted with a steel blade. Process for 30 seconds. Add the basil leaves, salt, and pepper. With the processor running, slowly pour the olive oil into the bowl through the feed tube and process until the pesto is finely pureed. Add the Parmesan and puree for a minute. Serve, or store the pesto in the refrigerator or freezer with a thin film of olive oil on top.
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