Heat milk, honey, oil and salt over low heat until just warm. Meanwhile, combine the all-purpose flour and yeast in the bowl of stand mixer. Drizzle liquid into the bowl and beat on low for 1 minute. Add egg and beat on medium for 3 minutes. Add whole wheat flour and mix until just combined.
Form into a ball and place in a large, greased bowl. Cover with plastic wrap and place in a warm spot, allow to double in size, 1 1/2 to 2 hours.
Punch down down and let it rest for 5 minutes. Dump onto a floured surface. Divide dough into fourths. Divide each of those into fourths. Form each into balls, not rolling but pulling and pinching under. Place in a greased 13x9 pan. Cover with plastic wrap and allow to rise again until doubled, about 45 minutes.
Preheat oven to 400 degrees F. Bake rolls for 10 to 15 minutes, until golden brown. While rolls are baking mix together the butter and honey in a small bowl. Brush over the rolls right after pulling them from the oven.