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Step 1
Combine the starter, buttermilk, sugar, egg and salt in a mixing bowl. Mix on low speed to combine the ingredients. Add half of the bread flour and mix to combine. Switch to the dough hook if mixing on a stand mixer.
Step 2
With the mixer running on low speed, add the remaining bread flour until the dough gathers on the hook and begins to pull away from the sides of the bowl. Knead on medium for 3 minutes then reduce the speed to low. If mixing by hand stir in as much flour as you can with a wooden spoon, then knead the remaining flour in by hand.
Step 3
With the mixer running, toss in 4 tablespoons of the softened butter a tablespoon at a time. If working by hand, knead in the butter. Reserve the remaining butter.
Step 4
Mix on medium for 3 minutes, if the dough is still very sticky add a little flour. The dough will stick to the bottom of the bowl but should gather on the hook. Dump the dough onto a floured surface and knead to form a smooth ball. The dough should be soft and smooth.
Step 5
Transfer the dough to a lightly oiled bowl, turning once to coat the dough. Cover the bowl and set it aside at room temperature for 3 hours. Every hour or so check on the progress of the dough by folding it over itself in the bowl. This will help redistribute the yeast too. After about 3 hours the dough should be lively, elastic and airy. If the dough is still sluggish give it another hour or two at room temperature. At this point the dough can be refrigerated for up to 2 days.
Step 6
Line two half sheet pans with parchment paper or a silicone baking mat. Turn the dough out onto a lightly floured surface and roll the dough to form a long log shape. Using a sharp knife or bench scraper cut the dough into 24 pieces.
Step 7
Roll each piece of dough under your cupped hand to form a smooth ball. Place the rolls onto a parchment lined baking sheet. Melt the reserved butter and use half of it to brush the rolls. Cover and set aside in a warm spot to rise until nearly doubled in size and the dough springs back slowly when poked, about 1-2 hours. The rising will take longer if the dough was cold from the refrigerator. Meanwhile, preheat the oven to 375°F.
Step 8
Bake the rolls until they are golden brown and feel light when picked up. About 10-15 minutes.
Step 9
As soon as the rolls come out of the oven brush the tops with the rest of the melted butter. Enjoy warm or at room temperature.