Heat your milk in the microwave or on the stove until it is warm to the touch (around 100-110 degrees F), but not hot. Pour into the bowl of your stand mixer and add sugar and yeast. Stir and allow to sit for 5-10 minutes, or until yeast has gotten foamy.
Add egg, butter, flour, and salt to the yeast mixture, and turn your mixer on low until the dough has come together into a shaggy ball.
Turn your mixer up to medium speed and continue to knead the dough for 6-8 minutes, or until the dough is in a smooth ball and is only slightly sticky (you do not want it heavily sticking to your hands or the mixing bowl).
Transfer the dough to a lightly oiled bowl, and cover with lightly oiled plastic wrap or a damp cloth. Let the dough rise for 1-1 ½ hours at room temperature until doubled in size.
Once it has doubled, remove the plastic wrap from the bowl, and lightly punch down the dough to remove the excess air. Turn out the dough onto a lightly floured work surface.
Using a rolling pin, roll the dough into a 10-inch x 24-inch rectangle, and spread the butter with a butterknife or an offset spatula, leaving about a 1-inch border around the edge of the dough. Mix the brown sugar and cinnamon in a separate bowl, and sprinkle over the top of the butter and dough. Pat down gently.
Starting on the 24-inch side, roll up the dough tightly. Place the roll seam-side-down, and cut it into 10 (roughly) 2 1/2 inch sections with a sharp kitchen knife or a piece of unflavored dental floss. Place the cut rolls in a greased 9x13 baking dish, and let rise for 30-45 minutes.
After they have risen, preheat your oven to 350°F and pour 2 Tablespoons of melted butter and 2 Tablespoons of half-and-half around the rolls (into the bottom of the baking dish. This is what makes these rolls so moist and delicious.) Bake the rolls for 20-25 minutes until lightly golden brown.