Warm milk and unsalted butter to ~100-110℉ in the microwave. (temperature suggested to effectively activate yeast).
Combine warm milk and butter mixture, yeast, sugar, honey, egg and salt in a large mixing bowl (or stand mixer bowl). Whisk to combine.
Add bread flour. Using a stand mixer with the dough hook on, or your hands, knead dough until bread flour is folded into the dough. When done, dough should be slightly sticky but a big clump shouldn't stick to your fingers when you touch the dough with dry fingers. If dough is too wet, add more bread flour 1 tbsp at a time. (See Note 1)
Transfer dough to a greased large mixing bowl. Cover with a towel and let it rise in a warm spot for 1 hour.
ALTERNATELY - Combine dough ingredients in bread machine and run dough cycle.
After dough has risen, it should be at least twice its original size. Punch dough to remove air bubbles, then transfer dough to a floured surface. Roll dough into a long tube, then cut tube into 12 pieces – try to keep them about the same size (First, cut tube into half, then cut into quarters, and then divide each quarter into three pieces). Lightly knead each piece of dough and shape it into a ball.
Place each ball onto a 9' x 13' baking dish. See picture on how to place them. Cover with towel and let it rise in a warm spot for another hour.
Pre heat oven to 350℉. Bake for 20 minutes. (You may need to tent the top with foil mid-way through baking.)
While rolls are baking, combine softened salted butter and honey in a bowl.
Serve with honey butter.