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In the bowl of your stand mixer, combine the sourdough starter, water, and yeast.
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Weigh your flours; or measure them by scooping them into a cup and sweeping off any excess. Combine the flours, dry milk, salt, and sugar, then add to the mixer bowl with the starter and water.
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Fit your mixer with the paddle attachment and turn it to its lowest speed. Mix all the ingredients together for 2 to 3 minutes to make a sticky, cohesive dough.
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Stop the mixer, scrape the bowl, and switch to the dough hook. Add the butter, then turn the mixer up a speed or two and continue to knead until the dough is smooth and elastic, about 8 to 12 minutes longer. Try the windowpane test: you should be able to stretch a piece of dough until you can see through it.
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Cover the dough and let it rest in a warm place (75°F to 80°F) for about 4 hours. To de-gas and even out the temperature of the dough, stretch and fold it in the bowl two or three times during the rest. You can be fairly flexible in your timing of these; one stretch and fold per hour is ideal.
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Turn the dough out onto a lightly floured work surface and divide it into six equal pieces; if you have a scale, each piece should weigh about 120g.
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Shape the dough pieces into tight balls and place them on a lightly greased or parchment-lined baking sheet, or into the lightly greased wells of a hamburger bun pan.
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Press the balls gently to flatten them slightly; they should come close to filling the wells of the bun pan, if you're using it.
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Cover the buns and let them rise until puffy, about 4 hours in a warm place.
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Twenty minutes before you’re ready to bake, preheat the oven to 375°F.
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Uncover the buns and brush them with the beaten egg yolk/water mixture. Sprinkle with toppings.
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Bake the buns for 20 to 25 minutes, until golden brown and a digital thermometer inserted into the center of one bun reads at least 190°.
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Remove the buns from the oven and allow them to cool before serving.
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Store buns at room temperature for several days; freeze for longer storage.