Have water and milk at 80°F and all other ingredients at room temperature. Place dough ingredients in the pan in the order recommended by your bread machine manufacturer. Select the dough/manual cycle. Check dough consistency after about five minutes of kneading. The dough should form a soft, tacky ball. If it is dry and stiff, add water, 1/2 to 1 Tbsp. at a time. If it is too wet and sticky, add flour 1 Tbsp. at a time. When the cycle ends, continue to the next step.

Turn the dough onto a lightly floured surface and punch down to remove air bubbles. Divide into two equal pieces, then divide each half into three or four pieces. Shape each piece into a smooth ball. Place on a large, greased baking pan and flatten each ball to about a 4-inch diameter, allowing 1 inch of space between buns. Cover and let rise until an indentation remains after gently touching the dough, about 20 minutes.

Brush egg wash over the buns. Sprinkle tops with sesame seeds, if using.

Preheat oven to 400°F.

Bake for 10 to 12 minutes. Remove from the pan and cool on a wire rack.

Notes
Get the traditional bread-making method here. To keep buns tender and fresh, do not pull them apart until ready to use.

Hot Dog Variation
Shape each piece into a 6-by-4-inch rectangle. Starting with the longer side, roll up tightly, pressing the dough into the roll with each turn. Pinch edges and ends to seal. Place on a greased baking pan. Let rise and bake as directed above.