Add yeast to the bowl of a stand mixer and add 2 tablespoons of warm water along with a pinch of sugar. Let sit until the yeast foams, about 3-5 minutes.

In a separate bowl, whisk together the flour and salt and add to the egg mixture. Mix with a rubber spatula until the flour is absorbed, it will be very shaggy.

Add the dough hook and knead until smooth and does not stick to the sides of the bowl, about 5-6 minutes. It should not be sticky. Add to a buttered bowl and cover with plastic wrap. Let it rise in a warm area until doubled in size, about 1 hour.

Add olive oil to a saucepan over low heat. Add the minced garlic and ½ teaspoon salt and cook until it has softened, being careful not to brown it. Remove from the saucepan to cool. In a separate bowl, combine 4 tablespoons of softened butter with basil, oregano, 1 teaspoon salt, pepper and ½ cup of grated cheese and egg yolk, reserve the egg white for the egg wash. Add the cooled garlic and mix to combine.

When the dough has risen, place it on a large cutting board and roll it into a 10 x 14 inch rectangle. Spread the garlic mixture over the top of the dough leaving a ½ inch border on all four sides. In a small bowl, beat the egg white with a tablespoon of water and a pinch of salt. Brush the border with the egg white mixture. Roll the dough into a tight log.

Brush the top of the rolls with the egg wash and sprinkle with remaining ½ cup of parmesan. Bake at 350º for 30 minutes, until the top is golden brown.