Dissolve the yeast in warm water until foamy. Do not go onto the next step if your yeast hasn’t proofed properly.
In a large bowl of a stand mixer fitted with the dough hook attachment, combine 1 cup of buttermilk, ½ cup butter, egg, sugar, salt and the yeast mixture, then add 3 cups of flour. Knead on medium speed until smooth, about one minute. Add the remaining flour, a ¼ cup at a time, to form a soft dough.
Turn the dough onto a lightly floured surface. Knead the dough until it’s smooth and elastic, six to eight minutes.
Place the dough in a greased bowl, turning once to grease the top. Cover it with a clean, dry kitchen towel and let the dough rise in a warm place until doubled, about one hour.
Punch down the dough. Turn it onto a lightly floured surface. Using a knife or bench scraper, divide the dough into 20 equal-sized pieces. Shape the pieces into balls.
Place the rolls in a greased 13x9-inch pan. Cover the top of the pan with a clean and dry kitchen towel, and let the rolls rise in a warm place until almost doubled, about 45 minutes. Preheat your oven to 350° during the last 10 minutes of rise time.
Brush the rolls lightly with the butter. Bake the rolls until they’re golden brown, 20 to 25 minutes. Cool the rolls at room temperature in the pan for 20 minutes. Remove the rolls to a wire rack, and serve warm.
