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1
Mix yeast, 1/2 cup of flour, sugar, and warm water in a bowl. Cover and let rest in a warm place until bubbling, about 15 to 20 minutes.
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2
Stir in salt, olive oil, and egg. Mix thoroughly and stir in remaining 1 3/4 cup flour to form a loose, sticky dough that pulls away from the sides of the bowl. Cover with a damp towel and let rise in a warm place until doubled in size, about 1 to 1 1/2 hours.
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3
Punch down and scrape the dough from the sides of the bowl. Turn onto a lightly floured surface. Sprinkle with more flour and shape into a rectangle. Roll out to an approximately 10x12-inch rectangle, about 1/2-inch thick. Brush with melted butter; sprinkle with garlic, Parmagiano-Reggiano cheese, black pepper, cayenne, and parsley.
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4
Press flat one long edge of the rectangle and brush with water. From the opposite end, roll evenly into a log. Press the seam together to seal.
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5
Cut into 8 rolls. Transfer to a baking sheet, cut side up. If necessary, cut an 'X' in the top of each roll to expose filling.
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6
Preheat an oven to 400 degrees F (200 degrees C).
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7
Brush each roll with olive oil. Sprinkle with more cheese. Cover and let rise until slightly puffed, about 20 to 30 minutes.
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8
Bake in preheated oven until the tops are golden brown, about 20 minutes.
