In a large bowl, mix the flour, sugar, salt and yeast until combined. Add the water, milk and melted butter and mix well. Stir in the egg. Transfer dough to a lightly floured surface and knead for about 3 minutes. Shape dough into a ball and allow to rest for 5 minutes.
In a small bowl, combine the softened butter, garlic, parsley and 1 cup of grated Parmesan. Set aside.
On a lightly floured surface, roll the dough out into a rectangle. Cover with the garlic paste, then roll up into a log. Cut log into slices approximately 1 inch thick.
Place slices into a round, greased baking pan. Sprinkle with the rest of the Parmesan and allow to rest for 20 minutes.
Preheat oven to 390 degrees. Bake bread for 20 minutes or until golden.