In the bowl of a stand mixer, stir together the milk, honey, and yeast. Let rise until the yeast is bubbly and poofy, about 5-10 minutes. Whisk in the butter, egg, cheddar cheese, and salt.
Attach the dough hook to your mixer. Measure in 2 cups of flour, then turn the mixer to its lowest speed. Add flour 1/4 cup at a time until the dough begins to pull away from the sides of the bowl and transform into a neat little ball. The dough should be tacky, not sticky. Continue to knead on low speed for 10-15 minutes.
Lightly grease a clean bowl with oil. Turn the dough into the bowl so both sides are coated with the oil, then cover with plastic wrap or a clean towel. Let rise in a warm, draft-free area for 60-90 minutes or until doubled in size.
In a small bowl, combine the butter, honey, and salt.
Preheat oven to 400 degrees. Lightly grease a 9 x 13 inch baking dish.
Punch down the dough and divide in half. Flour a clean work surface and roll the dough into a 1/4 inch thick square. Cut into 6 strips. Brush the length of each strip with the honey butter and, starting from the short end, roll tightly down the entire length. See photos for reference. Set each roll seam-side down into the casserole dish with about 1/2 inch or so between each. Repeat with the remaining ball of dough. Cover the dish and let the rolls rise for 30 minutes.
Uncover the dough and brush the tops of the rolls with a little of the honey butter. Bake for 15-18 minutes until the tops are golden brown. If the tops begin to brown too much, tent loosely with foil and continue to bake. Serve the rolls warm with additional honey butter, as desired.