In a cup or small bowl, combine warm milk, sugar, and yeast. Let the yeast proof and activate while preparing other ingredients. (Optional but preferred over using cold milk from the refrigerator).
Using a stand mixer or food processor, mix flour, egg, 1/3 cup melted butter, and salt.
Add the milk mixture and process until a smooth, sticky dough forms—stickier and wetter than regular bread dough.
Place the dough in a greased bowl, turning to coat all sides. Cover with a towel and let it rise until doubled in size.
Once doubled, punch down the dough and transfer it to a floured board. Let it rest for 10 minutes.
Roll out the dough into a large, flat rectangle, approximately 1/2 inch thick.
Cut the dough into 16 portions with a sharp knife and place them on a greased baking sheet. Let them rise again until doubled.
Preheat the oven to 375 degrees.
Bake the rolls for 10 minutes on the greased baking sheet until they are light brown.
Optionally, brush the tops of the rolls with the remaining 1/4 cup melted butter before serving.
Prepare honey cinnamon butter by combining butter, cinnamon, honey, and powdered sugar until well blended.
