Heat your oven to 425 degrees F.
In your KitchenAid, mix the yeast and warm water until dissolved - allow to sit for 5 minutes to proof (it should get frothy).
Add the sugar, oil, egg, and salt - stir just until combined.
Add the flour, and mix on low - once it is blended, continue to mix with your dough hook until it pulls away from the sides (2-3 minutes). Turn out on a lightly floured surface and knead (by hand) for 2-3 minutes - you might need to add more flour.
The dough should be soft and elastic - divide into 12 equal portions and shape each into a smooth ball. Pull the seams down to the bottom to make the tops very smooth.
Place the rolls seam side down, and 3-4 inches from each other on a greased baking sheet.
Cover with a tea towel or, lightly greased plastic wrap. Let sit for 10-15 minutes or until larger in size.
Uncover and brush with the egg wash mixture. Sprinkle with sesame seeds or kosher salt (on the tops).
Bake for 10 minutes to see them turn nice and golden. OR, opt for 15 minutes for a dark, rich color (still a very soft roll!)