In a small saucepan set over medium low heat, add milk, butter and honey. Heat until butter is melted and mixture reaches between 120°-130°F.
In the bowl of stand mixer fitted with a dough hook attachment (or in a large bowl if mixing by hand), combine all of the whole wheat flour, 1/2 cup of the all-purpose flour, the salt and yeast.
Add milk mixture to bowl and mix with a dough hook or spoon until combined to form a very wet dough. Add eggs and mix until incorporated.
With mixer running on medium speed, add remaining all-purpose flour a few tablespoons at a time until dough clears the sides of the bowl. You may not need all of the flour, you may need a little more. The dough should still be moist and sticky, but shouldn't come off and stick to your fingers when handled.
Knead dough with the mixer or by hand for another 3-4 minutes until smooth and elastic.
Cover dough with plastic wrap and let rise in a warm place until doubled, about 1 hour.
Gently punch down dough and knead a few times, then portion dough into 12 rolls and smooth tops. (I use a scale to make sure all rolls are the same size.)
Place shaped rolls in a greased baking dish and cover with plastic wrap. Let rise until doubled again, about 30 minutes more. Meanwhile, preheat oven to 350°F.
Bake rolls until tops and golden brown, about 20 minutes.
For the glaze, combine melted butter and honey brush onto rolls right when they are hot from the oven.
Rolls are best served when they are warm and fresh, but will keep at room temperature for several days.