Place 1 cup of the flour, rosemary, sugar, salt, and yeast in a large bowl or the bowl of an electric mixer and stir together. Add 3 Tablespoons olive oil and the warm water. Using electric hand beaters of your stand mixer, beat mixture on medium speed for 3 minutes, scraping the bowl occasionally. Slowly add an additional 1 1/2 cups of flour to the mix, stirring to combine. Add the last 1/2 cup of flour if necessary--the dough should be soft and just a tad tacky. It shouldn't stick a lot to the sides of the bowl. I usually have to add the entire 3 cups of flour.
Lightly flour a work surface and turn dough out onto the surface. Flour your hands then knead dough for 5-8 minutes or until it is smooth and springy. You may need to add a little more flour as you go to keep it from sticking. Place dough in a large, lightly oiled bowl and cover it loosely with plastic wrap. Place in a warm place to rise for about 30 minutes or until doubled in size.
Grease 2 cookie sheets with oil or cooking spray.
Gently punch down the dough until it deflates. Divide the dough in half, place each half on a cookie sheet, then use your fingers to flatten and shape each dough ball into a 10 inch round circle. Cover loosely with plastic wrap and allow to rise another 30 minutes or until dough is puffed, and about doubled in height.
Heat oven to 400 degrees. Use the pads of our fingers to make deep depressions about 2 inches apart in rings around the outside of the dough. Gently brush surface of the dough with oil. Sprinkle with Parmesan cheese. Bake 15-20 minutes or until golden brown.
This bread can be sliced and served immediately or cooled, wrapped in saran wrap, and used within 3 days. For reheating or for dipping, I recommend slicing the dough into thin strips and broiling for 2-3 minutes or until crisped and lightly browned. For dipping, mix good quality olive oil with a teaspoon of dried Italian herbs and minced garlic or garlic salt in a shallow bowl or plate.