Combine 4 cups bread flour and yeast in a large bowl. Stir in water and mix until a soft, sticky dough forms, adding a little more flour if necessary. (I know it says 6 cups flour but don't feel the need to use it all).
Cover with a damp tea towel and let rest 20 minutes.
Mix in olive oil, white wine, 2 Tablespoons rosemary, and salt. Stir in enough flour to make a soft dough. Turn dough out onto a generously floured surface and begin to knead, sprinkling with more flour as needed to keep dough from sticking to your work surface and hands. Knead for 7 to 8 minutes.
Place the dough in a straight sided plastic container with a snap on lid and let rise until doubled, about 1 to 1-1/2 hours. The ideal room/dough temperature for rising dough is about 75 degrees.
After 30 minutes, place a baking stone in the oven and heat to 450 degrees.
Scrape the dough out of the container onto a lightly floured work surface and divide it into two balls. Place the dough balls on pieces of unbleached parchment paper and flatten each one into a disk or oval about 1/2" thick. Note: I can fit two ovals (but not two rounds) on my rectangular baking stone at one time. If you can only bake one focaccia at a time, set the other one in a cool place or the refrigerator while the first one bakes; or you can always cut the recipe in half.
Generously drizzle the dough with olive oil and use your fingers to spread it evenly, then dimple the dough all over with the pads of your fingers and scatter the remaining 2 Tablespoons of rosemary and the Pecorino Romano over it.
Cover focaccia with a damp tea towel or plastic wrap and let rise for about 30 minutes, or until the dough springs back slowly when you press a finger into it.
Slide the focaccia onto the hot baking stone and bake 10 minutes, then lower the temperature to 375 degrees and bake for another 15 minutes, or until the crust is golden. Cool on a wire rack 5 to 10 minutes before serving. Focaccia is best when eaten the same day it's baked, but it freezes beautifully.