Pierce potato several times with fork. Microwave on high until tender, turning once, about 12 minutes.
Cut in half. Scoop flesh into small bowl; mash well. Measure 2/3 cup (packed) mashed potato; cool (reserve extra potato for another use).
Combine 2 1/2 cups flour, half of rosemary and 1 teaspoon salt in processor; blend until rosemary is chopped, about 1 minute.
Add potato; blend in, using about 25 on/off turns.
Combine 1 cup warm water and sugar in 2-cup glass measuring cup; sprinkle yeast over.
Let stand until foamy, about 5 minutes. Stir 3 tablespoons oil into yeast mixture. With processor running, pour yeast mixture into flour mixture. Process until smooth, about 1 minute. Scrape dough out onto lightly floured surface. Knead until dough feels silky, sprinkling with more flour as needed, about 1 minute.
Place dough in large oiled bowl; turn to coat. Cover with towel; let rise in warm area until doubled in volume, about 1 hour.
Position rack in center of oven and preheat to 450°F.
Brush large baking sheet with oil. Punch down dough; knead 30 seconds on lightly floured surface. Stretch or pat out dough to 12-inch round.
Transfer round to prepared baking sheet. Press dough all over with fingertips to dimple.
Brush with 1 tablespoon oil. Press olive halves, cut side down, into dough.