Preheat your oven to 375°F (190°C) and line a baking sheet with parchment paper. This helps the cheese straws crisp up without sticking to the surface.
Dust your work surface lightly with flour. Take the puff pastry and roll it out into a rectangle. Aim for about ¼ inch thickness, so they bake up flaky and crispy.
Spread the olive tapenade evenly over the entire surface of the pastry. This will add a savory base to your cheese straws.
Beat the egg in a small bowl. Brush the pastry lightly with the egg wash. This step will help the straws achieve that golden, shiny finish.
Sprinkle the grated cheeses—Parmesan and sharp Cheddar—over the top of the pastry, followed by the poppy seeds. Gently press the cheese into the pastry with your rolling pin.
Cut the pastry into thin strips, about 1-inch wide. Carefully twist each strip into a spiral shape. Be gentle to maintain the layers and not lose the cheese filling.
Place the twisted strips onto the prepared baking sheet, spacing them out so they don’t touch during baking.
Bake for 12-15 minutes, or until they’re golden and crispy. Keep an eye on them to make sure they don’t burn.
Cool slightly on a wire rack before serving. These cheese straws are best served warm, but they’ll also hold up well at room temperature.