Gather all your ingredients so that you have everything close at hand on the counter or table.
Prepare the Dough
In a large mixing bowl, mix with a dough hook (or stand mixer and kneading hook) the sourdough starter, warm water, large eggs, softened butter, brown sugar, kosher salt, wheat gluten, and instant yeast.
Mix in the whole wheat flour, and 2 cups of all-purpose flour. Knead for 5-7 minutes until dough comes together, adding remaining flour as needed to form a firm ball.
Transfer dough to a greased bowl and cover with plastic wrap. Place in a warm area to rise for 60-90 minutes, until doubled.
Make the Hamburger Buns
Turn dough onto a lightly floured surface and punch 2-3 times. Divide the dough into ten equal pieces. Roll each into a ball and flatten to about 1-inch thick.
Place flattened balls on a baking sheets lined with parchment paper or silicone baking mats. Cover with a clean tea towel and let rise for another 30-40 minutes until puffy. Near the end of the rising time, preheat oven to 400 degrees.
In a small bowl, combine egg and water to make egg wash. Gently brush egg wash over the buns and sprinkle with sesame seeds.
Bake in preheated oven for 15-20 minutes until golden brown. Cool on wire racks and slice before using. Makes 10 buns.
Notes
*Unless otherwise indicated, all butter used on this recipe site is salted.