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Prepare a cookie sheet with parchment paper. Assemble all the ingredients. Use exact measurements. Do not substitute ingredients and follow the recipe exactly and you will have buns like hotdog buns in my photo!
Rinse a large mixing bowl with hot water to warm it up. Add warm water, oil, sugar and the yeast. Set the timer for 15 minutes.
While you are waiting for the yeast to work, measure your flour and add the one teaspoon of salt to the flour and mix well. Beat the egg.
After the 15 minutes is up and the yeast has had a chance to work, add egg and the bread flour a little at a time to the yeast mixture with a whisk until it starts to get thick, and then trade your whisk for a wooden spoon and finish adding the rest of the flour or as much as needed to make a dough you can roll. It will be a nice tender dough.
Turn the dough out onto a lightly floured board. Roll to about 3/4 inch thick and cut out with a 4 inch glass or a clean can. Transfer the cut out dough to the parchment paper. If you want hotdog buns, turn the sides down and under to overlap and lay on the parchment paper. If you want hamburger buns, use the entire circle and place it on the parchment paper.
Brush tops of buns with the melted butter. Dont' skip this step because it makes them like store bought buns!
Let buns rise in the oven with the light on for about ten minutes. Then pre-heat the oven to 425 degrees and bake buns 10 minutes. (for inexperienced bakers: you DO remove the buns from the oven before you preheat the oven!) Enjoy!
Cook's Tip: These buns freeze really well for later use.