Combine yeast, 2 tablespoons sugar and water in 2-cup liquid measuring cup; let stand 5 minutes.
Combine yeast mixture, 2 cups flour, 1/4 cup oil, eggs, remaining sugar, salt and parsley in bowl of heavy-duty mixer using dough hook, if available.
Beat at medium speed 2 minutes. Gradually stir in 1/2 cup cheese and remaining flour until a soft dough forms. Cover and let rise in a warm place (85°F), free from drafts, 1 hour or until doubled in bulk.
Meanwhile, cut off pointed end of garlic bulb; place bulb on a square of aluminum foil. Drizzle with 1 tablespoon olive oil. Wrap bulb in foil. Bake at 350°F 1 hour; cool 5 minutes. Squeeze pulp onto foil and set aside.
Punch dough down and place in a large lightly greased bowl. Cover and let rise in a warm place, free from drafts, 45 minutes or until doubled in bulk.
Place dough on lightly floured surface. Fold garlic pulp into dough. Form dough into rectangular loaf shape or to desired shape. Place, seam side down, on lightly floured baking sheet. Brush with remaining oil and sprinkle with remaining cheese.
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