In a large bowl, combine 2 cups of bread flour, 1 tablespoon of sugar, 1 3/4 teaspoons of salt, and 2 packages of active dry yeast. Stir to combine.

Add 2 cups of very warm water (120° to 130°) and 2 tablespoons of extra-virgin olive oil to the dry ingredients.

Beat with an electric mixer at low speed until blended, then increase the speed to medium and beat for 2 minutes.

Gradually stir in enough of the remaining 3 1/2 cups of bread flour to form a soft dough.

Sprinkle 1/4 cup of bread flour over a clean work surface. Turn the dough out onto the floured surface and knead until smooth and elastic, about 10 minutes.

Place the dough in a bowl coated with vegetable cooking spray, turning to coat the top.

Cover the bowl and let the dough rise in a warm place (85°F), free from drafts, for 1 hour, or until doubled in size.

In a food processor, combine 1 cup of tightly packed fresh parsley, 2 green onions (cut into 2-inch pieces), and 2 cloves of garlic (halved).

Process for 20 seconds.

Add the remaining 1/2 teaspoon of salt, 2 tablespoons of extra-virgin olive oil, and 1/4 teaspoon of freshly ground pepper to the food processor.

Process for 15 seconds to create the pesto mixture.

Punch down the risen dough and divide it in half.

Sprinkle 1 tablespoon of bread flour over the work surface.

Roll one portion of the dough into a 16- x 10-inch rectangle.

Spread half of the parsley mixture (pesto) over the dough, leaving a 1-inch border.

Sprinkle with 1/4 cup of grated Parmesan cheese.

Roll up the dough tightly, starting at the long side.

Pinch the seam and ends to seal the loaf.

Repeat the procedure with the remaining dough and pesto mixture.

Place the loaves, seam side down, on a baking sheet coated with vegetable cooking spray.

Make 1/4-inch-deep slits in each loaf.

Cover the loaves and let them rise in a warm place, free from drafts, for 35 minutes, or until doubled in size.

Brush the loaves with lightly beaten egg white.

Bake at 375°F for 30 minutes, or until the loaves sound hollow when tapped.