Step 1: Prepare the Yeast Mixture - In a small bowl, combine the lukewarm milk and honey. Sprinkle the yeast over the top and let it sit for about 5-10 minutes, until frothy.
Step 2: Combine Dry Ingredients - In a large mixing bowl, whisk together the whole wheat flour, all-purpose flour, and kosher salt.
Step 3: Mix Wet Ingredients - In another bowl, beat the large egg and add the canola oil. Combine it with the yeast mixture once frothy.
Step 4: Combine Wet and Dry Ingredients - Pour the wet mixture into the dry ingredients. Stir until a shaggy dough forms.
Step 5: Knead the Dough - Transfer the dough to a floured surface and knead for about 8-10 minutes.
Step 6: First Rise - Place the kneaded dough into a lightly greased bowl, cover it, and let it rise for about 1 hour.
Step 7: Shape the Buns - Punch down the dough, divide into 8 pieces, and shape into buns.
Step 8: Second Rise - Cover the shaped buns and let them rise for another 30-45 minutes.
Step 9: Preheat and Prepare for Baking - Preheat your oven to 375°F (190°C) and brush the tops of the buns with the egg wash.
Step 10: Bake - Bake the buns for 15-20 minutes, or until golden brown.