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First, make the levain. Warm the heavy cream in a large, microwave safe bowl for about 45 seconds. It should feel like warm bath water, about 100 degrees. Gently stir the yeast into it and let it bubble for a minute. Then stir in the flour until it becomes a soft dough. Cover it with plastic wrap and let it ferment for 45 minutes in a warm, dry place. When the time is almost up, start on the pate.
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Combine the butter, sugar and salt in the bowl of a stand mixer. Beat them together until fluffy with the paddle attachment. Add in the eggs and egg yolks one at a time. Then turn the speed to low and slowly add in the flour just until it disappears. Switch to the dough hook and add in the fermented levain. Let the hook work the dough for 10-15 minutes until it becomes smooth and elastic and pulls away from the sides of the bowl.
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Wash out the bowl you used to make the levain, or get out a fresh bowl and grease it well with butter. Transfer the dough to the buttered bowl and cover it with plastic wrap. Set it aside to rise for an hour, until doubled in size. Punch it down, cover it in plastic again and put it in the refrigerator for another hour. Punch it down one more time, cover it again and let it sit in the refrigerator overnight.
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The next day, get out three loaf pans and spray them well with cooking spray. Take out the dough and pat it out into a square that is about two inches thick on the plastic wrap that you covered it with. Cut it into thirds, then cut each third into thirds. Round each piece into a ball and put three balls of dough into each loaf pan. Let them sit in the loaf pans to rise one more time for an hour.
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When the hour is up, pre-heat the oven to 375 and put the three loaf pans on a sheet tray. Brush the tops generously with egg wash, then bake them for about 30 minutes. They should be completely golden brown on top and baked through. Immediately brush them with the melted butter. Let them cool for 10 minutes or so, then turn them out onto racks to finish cooling. Use the bread in countless ways! You can freeze what you are not going to use immediately.