Mill your hard white wheat flour on the finest setting of your grain mill.
Measure out warm water and melt your butter.
To the bowl of a stand mixer, add the flour, salt, sugar and warm liquids. Mix just until all flour is moistened. Let autolyse for 20 minutes.
After the 20 minute autolyse, add the yeast and egg to your bowl and begin mixing. If using the Ankarsrum mixer, fit with the roller and scraper. You can use the dough hook on other style stand mixers.
Mix for 6-8 minutes until the dough begins to pull away from the sides and form a ball. It should be able to pass the windowpane test.
Cover and proof for 1 hour or until the dough has doubled in size.
After the dough has risen for 1 hour, it is time to shape. Weigh out 8, 97g portions. Shape buns by pulling dough in small sections up and into the center. Work your way around until you have creatd a smooth surface on the bottom. Pinch the dough in the center to seal.
Line your sheet pan with parchment paper
Unlike dinner rolls, you wanted to flatten slightly into a "disk".
Cover with plastic wrap and allow dough to proof for 20 minutes while you preheat oven to 400 degrees F.
With your remaining egg, add it to a bowl with a tsp of water and whisk until smooth. Brush the tops of your fresh milled hamburger buns and then sprinkle with sesame seeds. You can use poppy seeds, everything bagel seasoning or any other dry seed topping you prefer.
Bake at 400 degrees F for 15 minutes.
Allow to cool completely before splitting with a sharp bread knife. I only split mine when we are ready to make a hamburger. If I freeze them, I do so as a whole bun, unsplit.
Buns can be stored on the counter for 3 days in an airtight container or in the freezer for 3 months.