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In a large bowl or the pan of your bread machine set on the dough cycle, combine the yeast, water, honey, melted fat, salt, and 4 cups of the flour. Mix until a soft dough forms.
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Check the doughs consistency; if the dough sticks to your finger when you touch it lightly, add 1/4 cup of the additional flour and mix for another minute. Check the dough again, adding the remaining 1/4 cup of flour only if you need it; the dough should be soft, but not sticky.
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Knead for 6 to 8 minutes at medium speed in a stand mixer, or 10 minutes by hand, until it's smooth and bouncy.
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Cover the bowl and let rise for 1 hour, until doubled, or let the bread machine complete its cycle.
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Once the dough has risen, deflate it and divide into 10 pieces, roll into balls, and cover the pieces.
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Let them rest for 5 minutes before shaping the rolls into a football shape, tapering toward the edges; the rolls should be 5 1/2" long and 2" around at the center.
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Place the rolls onto a greased or parchment-lined baking sheet and cover with greased plastic. Allow the rolls to rise while turning the oven on and preheating to 400°F
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When the rolls are almost doubled in size, brush the tops and sides with egg wash. Using a greased knife, slash the rolls twice parallel to each other. Press down firmly with each slice.
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Bake for 20 to 22 minutes, until golden brown and the centers read 190°F on a digital thermometer. Remove from the oven and cool completely before slicing.
