In the bowl of a stand mixer (alternatively you can mix and knead the dough by hand), whisk together the warm milk, sugar, and yeast. Let stand 5 minutes. The mixture should start to foam and/or bubble. If nothing happens after 10 minutes, start over with new yeast.
Add the egg, flour, salt and 4 tablespoons butter to the bowl. Mix using the paddle attachment until combined. The mixture should be only slightly sticky when you touch it with your finger; if it is very sticky, mix in more flour, 1 tablespoon at a time, until the dough is only slightly sticky.
Switch to the dough hook and knead the dough on low speed for 8 minutes. Then transfer the dough to a lightly oiled bowl and cover with a clean kitchen towel. Let it rise for about 1 hour, until doubled in size.
Grease a 12-cup muffin tin with butter or cooking spray. Transfer the dough onto a lightly floured work surface and knead it briefly to release any large air bubbles. Divide the dough into thirds. Roll each third into a 12-inch long rope. Then cut each rope into 12 equal pieces. (You will have 36 small pieces of dough).
Roll each piece of dough into a smooth ball. Place 3 balls, seam side down, in each muffin cup. Cover the muffin tin loosely with a kitchen towel and let rise for 20-30 minutes.
Meanwhile, preheat oven to 375° F. Bake the rolls for 15-17 minutes, until golden brown on top and cooked through, rotating the pan halfway through baking.
Mix together the melted butter and honey. Brush the honey butter over the rolls as soon as the come out of the oven. Let cool for 5 minutes, then serve.