In large bowl or bowl of your stand mixer, weigh all cheddar cheese hot dog dough ingredients.
Knead in your stand mixer for 8 minutes or if you are kneading by hand, knead for 12 to 15 minutes until you have a smooth, non-sticky dough.
Add dough to a lightly oiled bowl and allow to proof on the counter or a warm place in your kitchen for at least 1 hour.
After an hour, roll out into hot dog shapes. I weigh my dough balls for consistency and shoot for 80 to 90 grams. You should be able to get 8 or 9 hot dog buns out of one batch of dough. If you don't have a scale, you can just make 8 similarly-sized dough pieces.
Place each hot dog dough piece onto a sheet pan in a row about 1/2 inch apart.
Cover your dough with lightly oiled plastic wrap or cover the sheet pan with another sheet pan. Let the shaped dough rise for 1 hour.
Near the end of your rise time, pre-heat oven to 350 degrees F (175 C).
Crack one whole egg into a small bowl and add 1 tablespoon of water. Beat the egg until everything is fully combined. Paint each bun very carefully with the egg wash, this helps the buns brown consistently.
Bake the rolls for 20 to 25 minutes. I typically peek into the oven to check for the bread color at 20 minutes.
Immediately after the rolls are removed from the oven, paint the tops with melted butter to help soften and flavor the crust.
Once the rolls are fully cool, store them in a bag or container for up to a week.