Place the milk, water, eggs, butter, salt, bread flour, sugar, and yeast in the bread machine pan in the order they are listed.
Select the dough cycle and hit start.
Line a baking sheet with parchment paper or spray a bun pan.
When the cycle is complete, divide the dough into 8 even pieces on a work surface sprinkled with 2 tablespoons of flour. Add more flour as needed.
Shape each piece into a tight ball and roll the dough into circles.
Arrange on the prepared baking sheet at least 1 inch apart.
Brush with the egg, and sprinkle with the sesame seeds.
Let sit at room temperature for 15 minutes.
Preheat the oven to 375 ° F while the buns are resting.
Bake for 15 to 18 minutes, until golden brown.
Cool slightly in the pan, and then transfer to a rack to cool completely.
If desired, split and toast before using.