Warm the milk in a small saucepan over medium heat until it's steaming and just beginning to bubble at the edges — about 180°F if you have a thermometer. Take it off the heat and stir in the 4 tablespoons of butter, the sugar and the salt until the butter melts. Let it cool until it's warm to the touch, about 105–110°F — hot milk will kill the yeast.

Sprinkle the yeast over the warm milk mixture, stir once, and let it sit 5–10 minutes, until foamy. If it doesn't foam, the yeast is tired — start over with a fresh packet.

Pour the yeast mixture into a large bowl, stir in the beaten egg, then add the flour 1 cup at a time, stirring until a shaggy dough forms.

Turn the dough onto a lightly floured counter and knead 8–10 minutes, adding just a dusting of flour as needed, until the dough is smooth, soft and elastic and springs back when poked. It should be slightly tacky, not sticky.

First rise: place the dough in a lightly greased bowl, turn it once to coat, cover with a clean kitchen towel, and let it rise in a warm, draft-free spot for 1 to 1 1/4 hours, until doubled in size.

Gently punch down the dough and let it rest 10 minutes — this makes it much easier to roll. Grease a 9x13-inch baking pan with butter.

On a lightly floured surface, roll the dough out to about 1/2-inch thick. Cut out rounds with a 3-inch biscuit cutter or a drinking glass, gathering and re-rolling the scraps once.

Melt the remaining butter. Brush the top of each round lightly with butter, then use the dull edge of a butter knife to crease each round just off-center. Fold the larger half over the smaller half so the top edge sits about 1/2 inch back, and press the folded edge gently to seal. This off-center fold makes the classic pocketbook shape.

Arrange the folded rolls in the prepared pan in 3 rows of 4, seam sides facing the same way, with the rolls just touching. Cover and let rise a second time for 30–40 minutes, until puffy and touching each other all over.

While the rolls rise, heat the oven to 375°F (190°C).

Bake 18–20 minutes, until the tops are deep golden brown and the rolls sound hollow when tapped.

Brush the hot rolls generously with the remaining melted butter. Let them rest in the pan 5 minutes, then serve warm — they pull apart best right from the pan.