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In a large bowl, combine flour, yeast, sugar, and salt. Add warm milk, egg, and softened butter. Mix until a soft dough forms.
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Knead on a floured surface for 6 to 8 minutes until smooth. Place in a greased bowl, cover, and let rise for 1 hour until doubled.
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Make the garlic butter: Melt 6 tablespoons butter and stir in minced garlic and parsley.
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Punch down the dough and divide into about 20 small pieces. Roll each into a ball.
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Dip each dough ball in the garlic butter, then arrange in a greased 10-inch cast iron skillet. Pour any remaining garlic butter over the top.
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Cover and let rise for 30 minutes until the rolls are puffy and touching each other.
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Preheat oven to 375 degrees F. Sprinkle Parmesan over the top if using.
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Bake for 22 to 25 minutes until golden brown on top. Serve warm from the skillet.