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In a stand mixer add the flour, salt, yeast and sugar.
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Add the eggs, milk and vanilla extract and mix together just until the flour is incorporated, the dough will be quite tough and lumpy at this point, this is normal.
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Using the dough hook attachment for your mixer begin adding the pieces of butter as the dough turns in the bowl. Continue until all of the butter is incorporated into the dough.
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Continue kneading until the dough is very smooth and elastic. Do not add additional flour.
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Cover and let rest and rise until double in volume.
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Turn the dough out into a lightly floured breadboard and knead for about 5 minutes before forming the dough into 16 individual balls.
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Place 8 balls each into two greased bread pans.
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Cover with a tea towel and let rise for a couple of hours or until it has risen to about an inch above the rim of the loaf pan.
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Brush the top with a little egg wash made from whisking together an egg with 2 tbsp water.
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Bake at 350 degrees F for about 30 -35 minutes until golden brown on top and the bottom has developed a good crust that releases easily from the pan.
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Once removed from the pan, cool on a wire rack for 15 minutes before serving warm.