To the bowl of a stand mixer, add 1 ⅓ cups warm water, 1 packet instant dry yeast, 1 tablespoon granulated sugar, 1 tablespoon olive oil, 1 ½ teaspoons salt, and 3 ⅓ cups all-purpose flour. Knead on low speed until combined. Once combined, turn the speed to medium and knead until the dough pulls away from the sides and bottom of the bowl and a smooth dough is formed, about 6-8 minutes. The dough should be soft, pliable, and tacky.
Place the dough in an oiled bowl and cover. Set in a warm place and let rise until doubled in size, about 1 hour.
Once the dough has doubled, punch it down and place it on the counter. Divide the dough into 12 even-sized pieces. Pinch the edges of the dough pieces into the center, then flip each dough ball over and roll it into a tight ball. Place the dough balls on a baking sheet lined with parchment paper. Cover the dough balls with plastic wrap or a damp towel and let them rise for 30 minutes, or until doubled in size and puffy.
Preheat the oven to 400 degrees Fahrenheit. In a small bowl, mix together 1 egg and 1 tablespoon water to make an egg wash. Brush the egg wash over the dough. If you would like, score each dough ball using a sharp knife or a bread lame. Make ¼-inch deep slashes across the top of the dough.
Place the rolls on the center rack in the oven and add a handful of ice cubes to the bottom of the oven. Quickly close the oven door and bake for 18-20 minutes; this will create steam and help create a chewy, crisp crust. Remove the rolls from the oven and brush with 2 tablespoons melted salted butter and serve.
Notes
Leftover and Make-Ahead Instructions
At Room Temperature: Store your rolls in a bread bag or wrap them in plastic wrap. They will stay good for up to 3 days.
In the Freezer: Place baked and cooled rolls in a ziplock freezer bag and freeze for up to 2 months. Thaw at room temperature.
Make Ahead: Make the dough, then refrigerate it overnight. The next day, shape into rolls and allow to double in size at room temperature before baking.