In a large bowl or the bowl of your mixer, weigh out and add your all-purpose flour, salt, and instant yeast and stir to combine all of your dry ingredients making sure there are no clumps.
Weigh the rest of your ingredients including the thinly sliced scallions and add them to the bowl.
If using a stand mixer, knead for 8 minutes on medium speed. If you are kneading by hand, you will need about 15 minutes of kneading after all the ingredients are incorporated together.
The dough will be a bit sticky.
Place your dough in a lightly oiled bowl and cover. Let dough rise in a warm place for 1 to 1.5 hours. The dough should be doubled in size.
Remove dough from bowl to a lightly oiled counter and divide into 4 pieces. I like to weigh my dough at this point to keep them all fairly consistently sized.
Roll each of your eight pieces of dough on the counter until you have 4 cylinders of dough roughly 9 or 10 inches long.
Add each log of dough to a parchment-lined sheet pan.
Cover your shaped rolls with lightly greased plastic wrap or a second sheet pan flipped over on top of the pan you're using. Allow them to rise for another hour or an hour and a half until they are nearly doubled in size.
Near the end of your final proofing time, preheat your oven to 375 degrees F (177 C).
In a small bowl crack your one egg and add one tablespoon of water. Whisk to combine. Paint this egg wash evenly on top of all of your rolls. Be careful not to deflate the dough and make sure you paint the mixture down the sides as well. This will help the rolls to have a shiny brown exterior.
Add a few pieces of thinly sliced green onion on the outside of each roll if you want it to be clear that there are scallions in each roll.
Bake your rolls for 15 to 20 minutes rotating the sheet pan halfway through the baking time. I typically bake for 8 minutes and then rotate and come back in another 8 minutes to see what my level of brownness looks like. At that point your rolls should be done all the way through, you're just trying to get them to the color you prefer.
Remove rolls from the oven and allow to cool before slicing.