Make the starter: Put the starter ingredients into a small saucepan. Heat to low, whisk constantly for about 5 minutes, until smooth, shiny, and slightly thickened. Transfer to a bowl and put in the fridge to cool.
Make the dough: Put the flour, milk powder, sugar, salt, and yeast in the bowl of a stand mixer fitted with a dough hook.
In a separate bowl, add the cooled starter, along with the milk, egg, and melted butter. Whisk to combine, and add to the mixer bowl.
Mix on low speed until ingredients are combined, and then increase the speed to medium. Continue mixing for about 15 minutes, or until the dough is smooth and elastic. It shouldn’t be sticky and should form a tight ball. To test, take a small piece of dough and stretch it in your hand until you can see through it without it breaking.
Transfer to a large, lightly oiled bowl and cover with a towel. Set the bowl in the warmest spot in your kitchen and let it rise for about 90 minutes, until the dough has doubled in size.
At this point, you can refrigerate the dough to use tomorrow, or cut into 9 equal sized pieces. If you’re chilling the dough, take it out and let it come to room temperature before forming into rolls.
Once you’ve cut your dough into rolls, roll them on a clean, dry surface until they are smooth and round. Spray a square baking pan with cooking spray and add the rolls to the pan. Cover with a towel and let rise in a warm spot for about an hour.
Preheat your oven to 350 degrees F. Carefully brush the rolls with the egg/milk mixture and bake for 20-25 minutes, until the rolls are a dark caramelized brown.
Remove from oven, brush with melted butter and sprinkle with coarse salt. Let cool slightly before removing and serving.