Preheat oven to 400 degrees F. Lightly coat 2 baking sheets with nonstick cooking spray or line with parchment paper. Heat a small heavy skillet over medium heat.
Add the poppy and sesame seeds and cook, stirring until they are aromatic and toasted, 2 to 3 minutes. Turn out onto a plate to cool. In a small bowl, whisk together egg white, oil and salt.
Lay a sheet of phyllo on a work surface with a short side toward you. With a pastry brush, lightly coat the lower half of the sheet with the egg-white mixture and sprinkle with 1 tsp. seeds. Fold the upper half over to cover the lower half.
Brush the right half of the folded sheet with egg-white mixture, sprinkle with 1/4 tsp. seeds and fold the left half over the seeds.
Brush the bottom half of the folded sheet with the egg-white mixture, sprinkle with 1/4 tsp. seeds and fold the upper half over. Finally, brush the top with the egg-white mixture and sprinkle with 1/4 tsp. seeds. Cut into 10 short strips using a knife or serrated pastry cutter.
With a wide spatula, transfer the strips to the baking sheet, placing them about 1/2 inch apart. Repeat the procedure with the remaining 5 sheets of phyllo, egg-white mixture and seeds. Bake the straws for 8 to 10 minutes, until golden and crisp. Transfer to a rack to cool.
The straws may be stored in an airtight container at room temperature for 1 week or in the freezer for up to 2 months.
Makes about 5 dozen straws.
19 calories per straw: 1 g protein, 1 g fat, 3 g carbohydrate; 23 mg sodium; 9 mg cholesterol.