In a microwave proof measuring cup or bowl, scald 8 oz whole milk. Add 1 oz unsalted butter to the milk and allow it to melt. Set the milk/butter aside to cool to about 100F.
Combine the milk/butter with 1 oz sugar, 1 ½ teaspoons table salt and 1 large egg in a mixer bowl. Sprinkle 2 ¼ teaspoons dry yeast over the mixture. Mix on low speed to combine the ingredients. Add 5 oz (1 cup) of the bread flour and mix until a thick batter is formed.
Switch to the dough hook and with the mixer running on low, add the remaining bread flour. Knead for 5 minutes until the dough clings to the hook and clears the sides of the bowl. If working by hand add as much of the flour as you can then turn the dough out onto a floured surface and knead.
Put the dough into a lightly oiled bowl, turning once to coat the surface of the dough. Cover with plastic wrap and set aside to rise until doubled in volume (1 - 1½ hours).
Turn the dough out onto a lightly floured surface. Divide the dough into 8 equal portions. Roll each portion to a ball. Place the dough balls onto a parchment lined baking sheet. Use the palm of your hand to flatten each ball to a disc about 1" thick. Alternately, you can run a rolling pin over each ball to flatten.
Cover the sheet pan and allow the rolls to rise until almost doubled in size (about 1 hour). Press a roll with your finger. If it springs right back it's not ready, if the dent slowly fills in the rolls are ready to bake.
Meanwhile, preheat the oven to 400 °F.
Brush the tops of the buns with egg wash. Sprinkle each bun generously with sesame seeds. Bake until the buns are golden brown and feel light when lifted off the sheet pan, about 10-15 minutes. Allow to cool completely before slicing.
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Notes
If measuring the flour by volume use the “dip & sweep” method. That is, dip the measuring cup into the flour bin, overfill it, then sweep away the excess.The buns freeze very well.For 1/4 lb burgers make 8 buns. For sliders estimate 12-16 buns.