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In a large bowl, stir together warm water and yeast. Let stand until creamy, about 10 minutes.
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In a Kitchenaid mixer with the hook attachment, mix together the warm milk, egg, softened butter, sugar, and salt.
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When the yeast/water mixture is foamy, add it to the sugar mixture.
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Stir in half of the flour. Then stir in the remaining flour, 1/2 cup at a time, until the dough has pulled away from the sides of the bowl. Knead with the hook attachment until smooth and elastic, about 8 minutes.
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Keep the dough in the Kitchenaid bowl. Cover with a moist cloth or loose plastic wrap and let rise in a warm place until doubled in volume, about 1 hour.
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Using the hook attachment, knead the dough for 3-5 minutes.
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Divide the dough into 12-16 equal pieces, and form into round balls. Place on lightly greased GLASS Pyrex at least 2 inches apart. Cover the rolls with a damp cloth or plastic wrap, and let rise until doubled in volume, about 40 minutes. Meanwhile, preheat oven to 325 degrees F.
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Bake for 30-35 minutes in the preheated oven, or until golden brown.
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Remove from oven and drizzle a small amount of honey over the rolls.
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Allow to cool in the pyrex.
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Note: If using a metal cake pan, increase the oven temperature to 375 and bake for 20-25 minutes.
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Alternative: instead of honey, 1/4 cup softened butter can be spread over rolls.