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Grease a large bowl and a 13 by 9 inch baking pan. Set aside.
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Heat milk to a warm 100 degrees F.
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Using the paddle attachment, mix flour, yeast, salt, sugar and butter in a stand mixer (Kitchen Aid if you have one) until the butter is broken down into pea-sized pieces. This will only take a minute or so. Pour the warm milk into the mixer bowl with the flour mixture and then add the beaten egg. Mix to combine. Take off the paddle attachment and attach the dough hook to your mixer. Knead the dough for 7 or 8 minutes until it is smooth and elastic. Transfer the dough to the oiled bowl you have already prepared. Cover bowl with plastic wrap and set in a warm place to rise and double in size. This should take about 90 minutes
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Once the dough has doubled, remove it from the bowl and put it on a lightly floured work surface. Divide the dough in half. Roll one of your two dough balls into a 8 by 12 inch rectangle. Brush the rectangle with melted butter, saving the rest to be brushed on top of the rolls after they are baked.
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Cut the 8 by 12 inch rectangle in half lengthwise. Working with one rectangle at a time, fold the long side of the dough over to about 1/2 inch of the other edge, so that the bottom edge sticks out about 1/2 inch beyond the top edge. Folded, your rectangle should now measure about 2 inches by 12 inches. Repeat with the other pieces of dough.
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Cut each of your folded rectangles into four 3-inch pieces so that you have 16 rolls.
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Place the rolls, smooth side up, in a lightly-greased 13 by 9 inch pan. You should place the rolls so that you have 4 rows of 4 rolls in the pan with the longer side of the rolls going down the longer side of the pan,
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Gently flatten the rolls to spread them out a bit so that they cover the bottom of the pan.
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Cover the pan with plastic wrap and let the rolls rise for about 45 minutes to 1 hour. The rolls should be puffy but not doubled.
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While the rolls are being allowed to rise, preheat your oven to 350 degrees F.
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Bake rolls for 20 to 25 minutes. They are done when they are golden brown and feel set.
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Remove rolls from oven, brush them with melted butter and sprinkle with sea salt.