Warm the milk in a small saucepan until a thermometer registers 110 degrees F. Pour into a medium bowl; sprinkle with the yeast and let soften, about 2 minutes. Sprinkle with the sugar and set aside until foamy, about 5 minutes.
Combine the flour and fine salt in the bowl of a stand mixer fitted with the dough hook. With the mixer on low speed, add the yeast mixture and butter and mix until the dough is slightly smooth and soft but still sticky, about 2 minutes. Coat a large bowl with cooking spray; add the dough, cover with plastic wrap and let rise at room temperature until doubled in size, about 1 hour.
Generously coat a baking sheet with cooking spray. Turn the dough out onto a lightly floured surface. Stretch into a 16-inch-long log, about 2 inches wide; cut into 8 even pieces. Roll and stretch each piece into a 6-inch-long rope, then wind into a coil; tuck the end underneath. Transfer the rolls to the baking sheet and cover with plastic wrap. Let rest at room temperature 15 minutes, then refrigerate until slightly puffed, about 2 hours.
Preheat the oven to 400 degrees F. Fill a large pot or deep skillet with 3 inches of water. Add the baking soda and 1/4 cup coarse salt and bring to a boil. Add half of the rolls and cook until slightly puffed, about 1 minute, flipping halfway through with a slotted spoon. Recoat the baking sheet with cooking spray and return the rolls to the baking sheet. Repeat with the remaining rolls. Brush the rolls lightly with the beaten egg, then sprinkle with coarse salt.
Transfer to the oven and bake until the rolls are deep golden brown, 18 to 20 minutes, rotating the baking sheet halfway through. Transfer to a rack and let cool 10 minutes on the pan, then remove the rolls to the rack to cool completely.