Warm up the milk in a small saucepan. Milk shouldn't be too hot, this should take about 1-2 minutes. If you have an instant read thermometer, temperature should be no more than 105℉.
Pour the milk, yeast, and sugar in a small bowl. Let it sit for 5-10 minutes until the yeast puffs up.
Add 1 egg, softened butter, salt, and milk mixture onto the dough or stand mixer with dough hook attached. Add 4 cups of flour.
Turn on the mixer to medium speed and knead for 8-10 minutes. After about 5 minutes of kneading, check the dough. It should be tacky but not stick to the walls of the bowl. If it is sticky, add 1 tbsp of flour at a time until dough stops sticking to the walls.
Remove the dough and place into a large greased bowl making sure the top of the dough is also greased. Cover and let rest in a draft-free spot for 1-1½ hours.
Generously grease a 9x13 baking dish with melted butter.
Preheat oven to 350℉
Once the dough has rested, deflate and remove it from the bowl and cut 12-13 medium sized balls. Pinch ends so it seals and rolls them under your hand for about 30 seconds. Place the rolls side by side leaving about 1/2 inch between each if you can.
Once all the dough is rolled into balls, cover and let it rest for 5-10 minutes. Meanwhile make the egg wash by whisking 1 egg (with egg white) in a small bowl and set aside.
Bake uncovered for 13-15 minutes. The buns will be done when you have an evenly layered light golden brown color across the top of the buns.
Remove from heat and let it cool for 10 minutes and enjoy!
Once completely cooled, store them in an airtight container at room temperature for up to 4 days.
