In the bowl of a mixer, combine 2 cups of the flour, sugar, salt and yeast. Stir to combine well.

Add the milk, water and butter into a microwaveable bowl, and heat on high for about 1 1/2 minutes, until the liquid temperature reaches 120°F-130° F (48°C-54°C). The butter may not be melted, but that is ok.

Start the mixer, and add a thin stream of the liquid until you have a very soft batter. Add the eggs and mix until combined, about 30 seconds. Stop the mixer, and add another 2 cups of flour. Also, change the mixing paddle of you mixer to the dough kneading hook. Start the mixer again, and allow the dough to begin to mix and combine well. Add enough of the remaining flour as the dough kneads until a stiff dough is formed. With an electric mixer you will only knead the dough for approximately 3-4 minutes total.

(If you would rather knead the dough by hand, simply stir the dry ingredients and the hot milk mixture together. You will start the same way, with 2 cups of flour. Once the initial ingredients are combined, add 2 more cups of flour, and turn the dough onto a floured surface. Continue to work more flour into the dough and knead well for 10 minutes.)

Once the dough is kneaded, place the dough in a clean, well greased bowl. Cover with a clean towel, and allow to rest in a warm place to rise (around 99°F or 37° C) for 1 hour.

Uncover the dough and punch it down. Depending on what you want to make , you can divide the dough into 10 portions for regular sized hamburger buns (approximately 4 oz (114 gr) each) or 20 portions (approximately 2 oz each or 57 gr) for hot dog or slider buns. Roll the portions into balls, and place on a baking sheet lined with parchment paper. Cover the buns lightly with a clean towel, and allow to rise for another hour.

Preheat your oven for at least 15 minutes to 375°F (190°C).

If desired, after they have risen, brush the tops of the buns with the egg wash, and sprinkle with sesame seeds.

When the buns have fully risen, bake them in the heated oven for 25 minutes, until they are golden brown with a firm crust. Remove from the oven, and cool on wire racks.