Let puff pastry stand at room temperature 40 minutes to thaw.
Heat oven to 400°F. Unfold pastry on work surface. Using pastry brush, brush pesto evenly over all of pastry, including edges. Cut pastry into 16 squares; cut each square in half diagonally, making 32 triangles.
Lightly spray 2 large cookie sheets with cooking spray. Gently arrange pastry wedges on cookie sheets. Sprinkle with cheese and nuts.
Bake 5 minutes. Reduce oven temperature to 350°F. Bake 8 to 10 minutes, until edges are golden brown. Top wedges with basil. Serve warm.