Dissolve yeast in warm water.
Add oil and sugar and let stand for 5 minutes.
Add egg, salt, and enough flour to form a soft dough.
Turn out dough onto floured surface and knead until smooth and elastic (3-5 minutes).
Divide into 10 pieces and shape into balls.
Space 3 inches apart on tray lined with parchment paper.
Cover with towel and let rest for 10 minutes.
Place dough balls in oiled 12-inch round cast iron dish and let rise until they have doubled in size or are even with top of the dish.
Whisk egg wash together and brush bun tops with the wash.
Bake at 450° in brick oven for 14-16 minutes.
Rotate dish in oven as needed to evenly brown bun tops