In a medium bowl, combine the yeast, sugar and warm water. Leave to sit for 5 minutes, or until foamy.
In a large bowl or bread mixer, add the yeast mixture, one egg, vegetable oil, salt and bread flour. Depending on the flour, you may need a little more or less, start with 2 ¾ cups and add an extra ¼ cup if the dough is too sticky. Knead for 5 to 10 minutes. Place in a lightly oiled bowl, cover with plastic wrap and leave to sit for 45 to 60 minutes in a warm area, or until doubled in size.
Knock back the dough and shape into 10 even balls. Place on a lined baking tray. Lightly spray plastic wrap with oil and loosely cover the tray, oiled side down. This will prevent the plastic wrap from sticking to the dough. Again, leave to rise for 30- 45 minutes, or until doubled in size.
Prepare the barbecue for indirect cooking over medium-low heat (170°C to 190°C). If using a Weber Q® barbecue, set up your barbecue with a convection tray and a trivet.
Using a basting brush, brush the lightly beaten egg over the bread rolls. Sprinkle the sesame seeds over the rolls.
Bake the bread rolls over indirect medium-low heat, with the lid closed, until the rolls are just golden and sound hollow when tapped, about 12-14 minutes.