Thaw puff pastry for 40 minutes at room temperature. Line 2 sheets with parchment paper.
Unfold 1 pastry sheet on lightly floured surface. Spread 2 tbsp pesto over pastry, top with 2 tbsp tomato, 2 tbsp walnuts, and 4 tbsp crumbled feta. Starting at long sides, fold pastry towards center leaving 1/4" space in center. Fold one side over the other, making a 4-layer rectangle. Repeat with remaining pastry sheet. Cover pastry rectangles with plastic wrap and refrigerate for 45 minutes.
Heat oven to 400°F Cut each rectangle into 15 1/4" slices. Place cut side down on baking sheets 2" apart.
Bake for 14 minutes or until golden, turning over halfway through baking. Remove palmiers from the baking sheets and cool slightly on wire racks. Serve warm.