In a large bowl add all of the bun ingredients. Stir until it forms a shaggy dough.
Turn dough on to the counter and knead for 3-5 minutes or until the surface of the dough is smooth.
Lightly oil the bottom of a large bowl and the surface of the dough ball. Place the dough in the bowl and cover with plastic wrap. Let the dough rise for 1-2 hours or until the dough doubles in size.
Using your fingertips, gently press on the dough to remove the gas.
Divide the dough into 8 equal pieces.
Take one piece of dough and cut 2/3 of it, draw up the edges and pinch it into a parcel. Use a cupped hand and cup the dough ball shaping it into tight a ball. UsiForm the remaining piece into a cylinder. Cut the cylinder in half and attach each piece to the ball so that they oppose each other form a sort of lemon shape.
Gently flatten the shaped dough and place on a parchment-lined baking sheet. Repeat the shaping for the remaining dough pieces.
Cover the buns lightly with plastic wrap and allow to rise in a warm spot for ~45 minutes or until noticeably puffy.
Preheat oven to 350˚F/177˚C.
Gently brush the risen buns with melted butter, then with the egg white mixture. Sprinkle on the sesame seeds.
Bake in a preheated 350˚F/177˚C oven for 15-18 minutes or until golden brown.
Gently brush the buns with more melted butter.
Hamburger
Divide the ground beef into 8 equal portions.
Heat a cast iron pan on medium-high heat for 3 minutes.
Place a ball of beef into the pan and using a metal spatula press the firmly to create a bun-sized patty.
Cook for 1-2 minutes with out moving, until you see blood on the surface of the patty.
Using your spatula scrape the bottom of the pan to loosen the patty and flip. Cook another 1-2 minutes or until no longer pink inside.
Hot Dog
Bring 3 cups of water to a boil in a medium sauce pan.
Add the hot dogs and cook for 3 minutes.
Assembly
Slice the cooled bun in half.
Cut the burger patty in half. Place it on the bottom bun leaving a space for the hot dog to go in the middle.
Nestle the hot dog between the hamburger patties.
Add a squiggle of mustard to the hot dog and top with lettuce, tomato, and onion. Cover with top bun and eat with gusto.