In the bowl of your stand mixer, add the milk, sugar, 2 eggs, and yeast.
Add the flour. Mix at the lowest speed, until a shaggy dough forms.
Increase the speed of the mixer to speed 2. Add the divided butter, one portion at a time, until all the butter is incorporated.
Add the salt. Continue kneading at speed 2, until smooth and elastic, about 15 minutes.
Shape the dough into a tight ball.
Transfer the dough to a lightly oiled bowl. Cover and let rest, until doubled in size, 1 hour 30 minutes. The dough can also rest overnight.
If doing an overnight rest, take out the dough from the fridge and lest rest at room temperature for 30 minutes.
Divide the dough into 8 equal-sized pieces. You can also divide into 16 pieces to make two smaller loaves.
Working with one piece at a time, flatten the dough lightly.
Evenly spread 10 grams (about 18 to 20 pieces) of butterscotch chips on the dough. If making smaller loaves, use half of the amount in each roll.
Fold the edges towards the center to create a ball.
Flip the dough seam-side down, and roll into a tight ball. Repeat with the remaining dough.
Grease a 9- by 5-inch loaf pan with butter. Arrange the rolls into the pan.
Cover and let rest, until doubled in size, about 1 hour.
Closer to baking time, preheat the oven to 180 degrees C (fan 160 degrees C).
Make the egg wash. In a small bowl, add the remaining egg and 1 tablespoon milk.
Brush the rolls with the egg wash.
Top with the remaining butterscotch chips.
Bake for 30 to 35 minutes, or until the internal temperature reaches 90 degrees C.
Let rest for 5 to 10 minutes, before removing from the pan. Let cool completely on a wire rack.