Make the buns: Heat the milk until lukewarm to the touch (over low heat in a saucepan or for 30 seconds in the microwave). Stir in the sugar to dissolve, then stir in the yeast. Let stand until foamy, about 5 minutes.

Meanwhile, mix the flour and salt in the bowl of a stand mixer. Add butter and beat on low with the paddle until crumbs form. Make a well in the center and add the foamy milk and the egg. Beat with the paddle on low until a shaggy dough forms. Switch to the dough hook and knead on low speed until the dough is smooth and elastic, 10 to 15 minutes, scraping the bowl and hook occasionally. The dough will be a bit sticky.

Butter a large bowl and scrape the dough into it. Cover with a clean kitchen towel and let rise in a warm place until doubled, about 1 ½ hours.

Meanwhile, prepare the scallions: Heat the oil in a small saucepan over medium-high until shimmering and almost smoking, about 5 minutes. Remove from heat, then add the scallions and salt carefully (they’ll splatter). Stir well. Let stand while the dough rises.

Roll the dough: Gently press down on the dough in the bowl to deflate it. Turn it out onto a lightly floured surface. Using a lightly floured rolling pin, roll it into a rectangle 20 inches wide and 12 inches long, with the wide side facing you. It will be a scant ¼ inch thick. Use a spoon to scoop the scallions onto the dough, reserving any excess oil. Spread the scallions to the bottom and side edges and leave an inch rim at the top. Line a rimmed baking sheet with parchment paper.

Shape the dough: Starting from the edge closest to you, roll the dough up in a loose spiral. Pinch the long seam to seal. Using a serrated knife, cut the roll with a sawing motion into 12 even pieces. Place them cut side up on the prepared sheet, spacing evenly apart.

Using your fingertips, gently pull the dough layers apart a bit and if the end is coming unraveled, tuck it under the spiral. Sprinkle the rolls generously with sesame seeds. Cover loosely with the clean kitchen towel and let stand in a warm place for 20 minutes or cover the pan with greased plastic wrap and refrigerate overnight.

Heat oven to 375 degrees while the spirals proof. (If the buns have been refrigerated overnight, let them sit at room temperature until they’re room temperature and puffed.)

Bake until golden brown, about 20 minutes. Immediately after they come out of the oven, brush them with the reserved scallion oil. Serve hot or warm.