Preheat the oven to 425°F. Grease a large baking sheet or line with parchment paper.

Activate the yeast:
In a large mixing bowl, stir together the warm water, yeast, oil (or melted butter), and sugar. Let the mixture sit for 5–10 minutes until it becomes foamy.

Tip: If the mixture doesn’t foam, your yeast may be inactive. Start fresh for best results.

Make the dough:
Whisk in the egg and salt. Gradually stir in 3 cups of flour, adding a bit more as needed until a soft dough forms. The dough should be slightly tacky but easy to handle.

Knead the dough:
Turn the dough out onto a floured surface. Knead for 5 to 7 minutes, or until the dough is smooth and elastic.

Shape the buns:
Divide the dough into 8 equal pieces for large buns or 12 for smaller buns. Shape each piece into a ball and gently flatten the tops.

Let them rise:
Place the buns about 3 inches apart on the prepared baking sheet. Cover loosely with a clean towel and let rise for about 15 minutes, or until nearly doubled in size.

(Optional) Finish before baking:
For a golden, glossy finish, whisk the extra egg with 1 tablespoon of water and brush it over the tops of the buns. Sprinkle with sesame seeds if desired.
If you plan to brush with butter after baking instead, skip this step.

Bake:
Bake for 8 to 12 minutes, or until the buns are golden brown.

Finish and cool:
Remove the buns from the baking sheet and place them on a wire rack. If you didn’t use the egg wash, brush the warm buns with melted butter for a soft, flavorful crust. Let cool before slicing.