Place oil and rosemary sprigs in a small bowl; microwave on high for 30 seconds. Let stand 15 minutes. Gently squeeze oil from rosemary; discard sprigs.
Lightly spoon flour into dry measuring cups; level with a knife. Combine 1/2 cup flour and yeast in a large bowl, stirring with a whisk. Add 1/2 cup warm water; let stand 20 minutes. Add rosemary oil, 2 cups flour, 1/2 cup plus 2 tablespoons warm water, chopped rosemary, and 3/4 teaspoon salt; stir until a soft dough forms. Turn dough out onto a lightly floured surface. Knead until smooth and elastic (about 8 minutes); add enough of remaining flour, 1 teaspoon at a time, to prevent dough from sticking to hands (dough will feel tacky).
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, 1 hour or until doubled in size. (Press two fingers into dough. If indentation remains, the dough has risen enough.) Punch dough down; form into a ball. Place directly on baking sheet. Let rest 5 minutes.
Preheat over to 500°.
Roll dough into a 12-inch circle. Arrange tomatoes on top of flatbread, leaving a 1/2-inch border. Sprinkle with cheese; gently press toppings into dough. Sprinkle with 1/4 teaspoon salt. Bake at 500° for 10 minutes or until golden brown.