Combine yeast, 1 cup of the flour, salt and sugar. In a microwave-safe bowl/cup, heat water and milk to 120° to 130°F.
Combine the dry mixture with the milk, water and oil in a mixing bowl with paddle or beaters and beat for 4 minutes on medium speed. Add egg; beat 1 minute.
Gradually add the remaining flour and knead with dough hook(s) 5 to 7 minutes until smooth and elastic. Place dough in lightly oiled bowl and turn to grease top. Cover; let rise until dough has doubled. Check at 60 minutes and continue checking every 30 minutes until doubled. For me it took almost 2 hours but I'm at altitude so nothing is the same!
Turn dough onto lightly floured surface; punch down to remove air bubbles. Divide into 8 equal pieces. Shape each piece into a smooth ball. Place on 2 large greased baking pans or use parchment paper. Flatten each ball to a 4-inch diameter, allowing one inch between buns. Cover; let rise until indentation remains after touching, about 20-30 minutes.
For glaze, whisk together egg and water and brush on rolls. Sprinkle with sesame seeds (optional).
Bake in preheated 400°F oven for 10 to 12 minutes. Remove from baking pan and let cool completely on wire rack before slicing