In large bowl of electric mixer, sprinkle yeast over warm water. Let stand until softened (about 5 minutes).
Add olive oil, salt, sugar and 1 1/4 cups of the flour. Mix to blend; then beat at medium speed until smooth and elastic (about 5 minutes). Gradually beat in about 1 cup more flour to make a stiff dough.
Turn dough onto floured surface; knead until dough is springy and small bubbles form just beneath the surface (5-10 minutes). Transfer to greased bowl, cover and let stand in a warm place until doubled in buld (about 1 hour).
Punch dough down; divide in half. Cut each half into 15 equal pieces. Flour work surface and palms of hands well; use palms to roll each piece on floured surface into stick about 12 inches long. Place about 3/4 inch apart on greased baking sheets. Brush each stick lightly with egg mixture; sprinkle with sesame seed. Let rise until puffy, 30-35 minutes.
Preheat oven to 325 degrees. Bake until golden (25-30 minutes). Allow breadsticks to cool on racks. Makes about 30 breadsticks.