In a microwave safe bowl, add milk and butter pieces. Microwave in 20 second increments until butter has melted and mixture is warm to the touch, but not hot (about 110℉).
Whisk in sugar and yeast and allow to rest for 5 minutes. Mixture will look foamy and bubbly. (If it's not foamy after 5 minutes, your yeast may be expired and rolls will not rise properly.)
Meanwhile, add flour, salt, and egg to a large bowl. Once ready, add yeast mixture to the bowl and stir with a wooden spoon until a sticky dough forms.
Turn dough out onto a lightly floured surface. Using floured hands, knead the dough for 10 minutes. Dough will look smooth, slightly tacky, and slowly springs back when gently pressed. (See notes below for stand mixer directions).
Transfer dough to a lightly greased bowl, tossing dough to coat all sides, and lightly cover. Allow to rise for about 1 hour at room temperature, or until doubled in size.
Line a sheet pan with parchment paper and set aside.
Punch dough down to release air. Divide dough into 8 equal sized pieces (use a bench scraper for easy dividing).
Roll each piece into a round, smooth ball. Place onto prepared sheet pan and gently press with your palm to create ¾" flat discs.
Lightly cover rolls with a towel and allow to rise at room temperature for about 1 hour.
Meanwhile, preheat oven to 350℉ and adjust rack to the center of the oven (so the tops and bottoms brown evenly).
Egg wash
Whisk egg in a bowl and brush over the buns. Sprinkle with sesame seeds.
Bake for 22-26 minutes, or until golden brown across the tops and the buns reach 195℉ in the center.
Allow to cool completely before slicing in half lengthwise with a serrated knife.
Notes
Stand mixer directions: Add ingredients to the bowl of a stand mixer fitted with a paddle attachment or dough hook. Mix on low until a soft, sticky dough forms. Beat on medium speed until the dough starts to pull away from the sides of the bowl (this takes about 2 minutes). If dough looks wet and sticky, add more flour, 1 tablespoon at a time, until dough comes together and looks soft and slightly tacky, not sticky. Beat for an additional 5 minutes. Dough should feel soft and slowly bounce back when pressed.
Overnight directions: After you've shaped your dough on the sheet pan, cover and transfer to the refrigerator to rest overnight. This replaces the second 1-hour rise in the recipe card. When you're ready to bake your buns, pull them out of the refrigerator while your oven preheats, add thee egg wash and sesame seeds, then bake as directed in the recipe card.
Storage: Keeps 2-3 days at room temperature, frozen for up to 3 months