1. Stir together 1/4 cup warm water and sugar in small bowl. Sprinkle yeast over surface. Let stand until foamy, about 5 minutes. Stir to dissolve yeast.
2. Mix flours, olive oil and salt in food processor with on-and-off pulses. Add yeast mixture and remaining 3/4 cup warm water. Process until soft dough; process 1 minute to knead. Remove dough to work surface; knead by hand about 1 minute, adding flour as needed to prevent sticking. Place in oiled bowl, turning to coat. Cover loosely with clean kitchen towel. Let rise in warm place until doubled in volume, about 1-2 hours.
3. Punch down dough. Let rest 5 minutes. On lightly floured surface, pat or roll dough into 12 x 8-inch rectangle. Cut crosswise into twelve 8 x 1-inch strips. Cover loosely. Let rise in warm place until puffy, 30 to 45 minutes.
4. To bake, heat oven to 375 degrees F. Lightly grease 2 baking sheets. Whisk egg white and 1 tablespoon water in pie dish. Place seeds in second shallow dish.
5. Dip 1 strip of dough into egg white, then roll in sunflower seeds to lightly coat. Place at one end of prepared baking sheet. Holding one end of strip, twist dough 6 to 8 times, if desired. Repeat with remaining strips, coating, and arrange 6 strips on each baking sheet, spacing 1 to 2 inches apart.
6. Bake in 375 degree F oven 25 to 30 minutes, reversing sheets halfway through, until golden brown and crusty. Transfer breadsticks to rack to cool. Reheat in 350 degree F oven 10 minutes. Makes 12 breadsticks.