In a small saucepan over low heat, warm the milk and butter just until the butter is melted. Remove from heat and let cool slightly—it should be warm to the touch, not hot.
In a large mixing bowl, combine the warm milk mixture with the honey, egg, and salt. Stir until well blended.
Add 2 cups of flour and stir until a thick batter forms. Sprinkle the yeast over the top and stir it in. Continue adding the remaining flour, ½ cup at a time, until a soft dough forms.
Turn the dough onto a lightly floured surface and knead for 5–6 minutes, until smooth and elastic. You can also knead in a stand mixer using the dough hook. (This is the method I prefer.)
Place the dough in a lightly greased bowl, cover, and let it rise in a warm place for about 1 hour, or until doubled in size.
Punch down the dough and turn it out onto a lightly floured surface. Divide the dough into 16–18 equal pieces and shape them into rolls.
Arrange the rolls side-by-side in a greased baking pan. Cover and let rise for another 30 minutes, or until doubled.
While the rolls are rising, preheat your oven to 400°F (200°C).Bake the rolls for 15 minutes, or until golden brown and the internal temperature reads 185–190°F (85–87°C).
Serve warm, or transfer the rolls to a wire rack to cool completely.