In stand mixer bowl, add water; stir in yeast and sugar. Let stand until foamy, about 10 minutes. Stir in oil. Add 1 cup flour and salt. Using a paddle attachment, blend on low speed for 30 seconds. Beat on medium speed for 3 minutes.
Switch to dough hook attachment. Gradually stir in enough remaining flour to make a soft dough. Knead until smooth and elastic, about 5 to 7 minutes.(NOTE: For hand mixing: following above steps, mix ingredients in large mixing bowl using a wooden spoon or dough whisk. Knead on floured surface until smooth and elastic.) Place dough in lightly oiled bowl and turn to grease top. Cover; let rise until indentation remains after poking dough with finger down to second knuckle, about 1 hour.
Punch down dough; cover with tea towel; let rest for 10 minutes.
On lightly floured surface, roll dough into 16x12-inch rectangle. Evenly sprinkle oregano, basil, garlic and cheeses over top, leaving 1-inch border around edges. Starting from long side, roll up into cylinder; pinch along edges and end to seal. Place onto lightly greased or parchment-lined baking sheet; loosely cover with plastic wrap. Let rise until indentation remains after touching.
Preheat oven to 375°F.
Remove plastic; lightly brush with olive oil, sprinkle with salt and rosemary.
Bake in center of oven for 35-40 minutes or until golden brown and sounds hollow when tapped on bottom. Let cool 10 minutes. Remove from pan; let cool on rack.