In the bowl of a large stand mixer fitted with a dough hook OR a large mixing bowl, dissolve yeast in warm water and milk. Let stand 5 minutes until foamy. Mix in melted butter, honey, egg, salt, whole wheat flour, and 2-1/2 cups all-purpose flour on medium speed or by hand with a wooden spoon until dough pulls away from sides of bowl into a ball (if dough seems too sticky, add additional flour by the tablespoon until it comes together)
Knead the dough in the mixer 6-8 minutes or by hand on a floured surface 10-12 minutes until dough is stretchy and elastic. Place in a greased bowl, turning once to grease top. Cover with plastic wrap and let rise in a warm place until dough is doubled, about 1 to 1-1/2 hours.
Adjust oven rack to middle and preheat oven to 375F. Line two baking sheets with parchment paper and set aside.
Punch risen dough down and divide into 12 equal portions. Roll each portion into a round bun and place each bun 4 inches apart on prepared sheet pans.
Use your hand to gently flatten each bun. Allow buns to rise in a warm place 20-30 minutes until slightly puffy.
Brush buns with beaten egg white mixture and sprinkle with sesame seeds. Bake hamburger buns at 375F 18-25 minutes until golden-brown.
Cool buns on sheet pan 10 minutes, then transfer to a wire cooling rack to cool completely. Enjoy!