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Step 1
Combine milk, butter, honey, salt and egg in a mixer bowl. Sprinkle the yeast over the mixture. Mix on low speed to combine the ingredients. Add the whole wheat flour and mix until a thick batter is formed.
Step 2
Add 1 1/2 cups of the bread flour until the batter is very thick. Switch to the dough hook or turn out onto a floured surface to finish by hand. Add enough of the remaining bread flour until the dough clings to the hook and clears the sides of the bowl. Knead for 2-3 minutes to develop the dough.
Step 3
Turn the dough out onto a floured surface and knead into a smooth ball. Set in a lightly oiled bowl, turning once to coat the surface of the dough. Cover with plastic wrap and set aside to rise until doubled in volume (1 - 1 1/2 hours).
Step 4
Turn the dough out onto a lightly floured surface and knead to form a smooth ball. Divide the dough into 6 or 8 equal portions (based on how big your burgers are). Roll each portion to a ball and set them a parchment lined baking sheet. Use the palm of your hand to flatten each ball to a disc about 1" thick.
Step 5
Cover the sheet pan and allow the rolls to rise until almost doubled in size (about 1 hour). Press a roll with your finger. If it springs right back it's not ready, if the dent slowly fills in the rolls are ready to bake.
Step 6
Meanwhile, preheat the oven to 400°F.
Step 7
Brush the tops of the buns with egg white. Sprinkle each bun generously with sesame seeds. Bake until the buns are golden brown and feel light when lifted off the sheet pan, about 10-15 minutes. Allow to cool completely before slicing.