Place 1½ cups water, 2 tablespoons sugar, and the yeast in a small bowl. Stir to combine.
Allow yeast water to sit for 5-10 minutes to activate the yeast until it's bubbly.
Pour the yeast water into the bowl of a stand mixer.
Add 2 cups of bread flour.
Use the dough hook to mix together for 4 minutes. Start on low speed until flour is incorporated then increase speed to medium.
Add salt and remaining flour to the bowl and mix on low. Once flour is incorporated increase speed to medium and mix for 6-8 minutes until you have a slack dough.
Add more water, 1 tablespoon at a time if the dough is dry and stiff.
When dough is smooth and soft, add the softened butter one tablespoon at a time until fully incorporated into the dough and the dough is smooth and shiny.
Mix on medium speed for an additional 2-3 minutes or until the dough pulls away from the sides of the mixing bowl.
Transfer dough into a greased bowl and cover loosely with plastic wrap.
Allow dough to rest for 1 hour or until it doubles in size.
Lightly flour work surface and turn dough out onto prepared work surface.
Cut dough into 8 equal sized pieces.
Shape each piece of dough into a log shaped roll and place on a baking sheet lined with parchment paper.
Cover rolls loosely with a piece of plastic wrap sprayed with non-stick spray.
Allow rolls to rest for 30 minutes.
Place a metal pan on the bottom rack of the oven. Preheat oven to 375℉.
Uncover rolls and baste them with an egg wash made with an egg and a tablespoon of water beaten together.
Score the top of each roll down the middle with a lame or a sharp knife.
Place rolls in the oven and add a cup of water to the metal pan on the lower rack in the preheated oven.
Bake rolls until light golden brown in color and they reach an internal temperature of 200℉, about 20-25 minutes.
Remove rolls from the oven and allow them to cool to room temperature before slicing into them.