Dissolve yeast in warm water in a large bowl; let stand 5 minutes.
Lightly spoon flour into dry measuring cups, and level with a knife. Stir 1 cup flour into yeast mixture. Cover and let stand 30 minutes.
Add remaining 2 3/4 cups flour, 1 teaspoon salt, and 1 tablespoon rosemary to yeast mixture; stir until a soft dough forms. Turn dough out onto a lightly floured surface, and knead until smooth and elastic (about 6 minutes). Place dough in a large bowl coated with cooking spray, turning to coat top. Cover and let rise in a warm place (85°), free from drafts, 40 minutes or until doubled in size. (Gently press two fingers into dough. If indentation remains, dough has risen enough.)
Punch dough down; divide into 12 equal portions. Roll each portion into a 4 1/2- to 5-inch circle on a lightly floured surface. Brush dough rounds with olive oil; sprinkle rounds evenly with remaining 2 teaspoons salt and 1 tablespoon rosemary.
Place dough rounds on grill rack coated with cooking spray; grill 3 to 4 minutes on each side or until puffed and golden.