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Grease a 9 x 13 baking tray.
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Warm the milk in the microwave or in a pan on the stove until it is approximately 110 degrees F. Whisk the warm milk together with 1 T. sugar and the yeast in the bowl of your stand mixer. Set aside (covered) for about 5 minutes.
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After 5 minutes, add remaining sugar, egg, butter, salt and 1 cup flour (I used bread flour) to the mixer bowl fitted with either the dough hook or the paddle attachment. (I used the dough hook.) Beat this mixture for about 30 seconds. Stop the mixer and scrape down the sides of the bowl with a rubber spatula. Resume beating and add the remaining 2 cups of flour. Continue mixing until the dough comes together as a ball and pulls away from the sides of the mixer bowl. This will take about 2 minutes.
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At this point you can either remove the dough from the bowl and knead it by hand on a lightly-floured surface for about 2 minutes or leave it in the mixer and beat it (with the dough attachment) for another 2 minutes.
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Remove the dough from the bowl (if using the dough hook) and wash and dry the mixing bowl. Grease the mixing bowl (I used grapeseed oil) and put the ball of dough into the bowl. Turn the ball of dough over so that all surfaces of the dough have a bit of oil on them. Cover with plastic wrap or a towel and let the dough sit in a warm place in your kitchen for 1 to 2 hours until the dough has doubled in size.
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When the dough has doubled, punch it down to remove the air from the dough and divide the dough into 14 to 16 equal pieces. Shape each of the dough pieces into a smooth ball with your hands. Arrange the dough balls on the greased baking sheet about 1 inch apart. Cover and let the dough rise until it is puffy. This will take about 1 hour.
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While the dough is rising, prepare your oven. Preheat oven to 350 degrees F. Arrange a rack in a lower portion of the oven. Bake the rolls for 20-25 minutes until they are golden brown on the top. Rotate the tray of rolls halfway through the baking.
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Remove rolls from the oven. Brush with melted butter. Let rolls cool for a few minutes before serving.