Make the tangzhong: Stir together bread flour and water in a small saucepan over medium heat until flour is dissolved and mixture is smooth with no lumps. Continue stirring until mixture thickens and reaches 150 degrees Fahrenheit (about 10 minutes). Remove from heat, transfer to a mixing bowl, and cover.
In another mixing bowl, whisk together flour, sugar, instant yeast, and sea salt then make a well in the middle of the bowl.
Pour the tangzhong, warm milk, and melted butter into the well and mix with kitchen spoon until a tacky dough forms.
Turn dough out of the bowl onto a floured surface then knead it for about 10 minutes or until dough is soft and elastic and easy to stretch.
Shape dough into a ball and place back into mixing bowl then cover with a damp towel and set aside in a warm spot to rest and rise. Meanwhile, line baking dish with parchment paper or grease and flour it.
Once the dough has roughly doubled in size (after about one hour), punch/press the middle of the dough to flatten out air and turn out onto floured surface.
Separate dough into 14 equal pieces then roll each piece into a ball and place into prepared pan.
Cover pan with damp towel and allow to proof until doubled in size (about 40 minutes). Preheat oven to 375 degrees farenheit.
Mix egg and 1 tablespoon water for egg wash and set aside. Uncover pan then place on center oven rack and bake for 15 minutes. Brush tops of rolls with egg wash the return to oven and continue baking for another 10 minutes or until rolls are golden brown and glossy.
Notes
Purpose of TangzhongTangzhong is a paste made from flour and water that originates in China and helps give bread a super soft texture, higher rise, and allows it to keep longer--not that I suspect you'll leave much in the way of leftovers!PreparationTangzhong dough is significantly less sticky than regular yeasted dough but I still recommend working on a floured surface and with floured hands.For the best results, let the dough rise in a warm spot in your kitchen. Near a preheating oven is great or if there's a sunny spot from your kitchen window, that works, too!StorageBecause of the tangzhong, these rolls can stay fresh at room temperature for up to five days. Beyond that, I recommend refrigerating in an airtight container for up to three more days.To freeze, I recommend separating the rolls and wrapping each one in aluminum foil. Place the wrapped rolls in an airtight, freezer-safe container before freezing and they will keep for up to one month once frozen.