In the bowl of the stand mixer (or large bowl if you don't have a mixer), add the milk, melted butter, eggs, sugar, yeast, and salt. Mix with a spoon until combined. If you are using active dry yeast (not instant yeast), you will need to let it sit for about 10 minutes and start to bubble before you add the flour. Instant yeast is ready to go, and doesn't need to sit.
Next, add the flour, and use the dough hook attachment with the stand mixer. Mix on low until the dough starts to come together. If the dough is staying sticky, add a little more flour. Once it starts to come together, mix on medium-low speed until the dough it smooth, but still soft, about 6-7 minutes.
If you don't have this, you will add the flour to the large bowl, and mix lightly with a spoon until it starts to come together. Once it starts to come together, finish the mixing with your hands, and knead lightly in the bowl until the dough comes together.
Once the dough is smooth, soft, and no longer sticky to the touch, shape the dough into a ball. Lightly oil or butter a large bowl, and turn the dough ball in it to coat lightly with butter. Cover the bowl tightly with plastic wrap, and let the dough rise for about 1 - 1 1/2 hours, until it's doubled in size.
When the dough is almost ready, make the filling. To do so, mix the cinnamon and sugar in a small bowl until combined. And make sure your butter is softened and ready.
Once this rise is ready, punch down the dough lightly, and put it on a prepared, flat, floured surface - I always clean and use my kitchen counter for this. Dust the top of the dough with a little more flour, and roll it the dough out to a rectangle, about 12" long, 10" wide, and 1/4" thick. Next, gently spread the softened butter across the top of the dough, covering the surface, and leaving about 1/2" border around the dough. Once it's butter, sprinkle the cinnamon sugar mixture on top, coating it evenly.
Get a little water on your fingers, and lightly water the 1/2" border of exposed dough. This will help it stick together once rolled. Next, roll the dough the longest way - in other words, when rolled it will still be 12" long. Cut the dough into 10 equal slices with a sharp knife. The sharp knife is important so it doesn't flatten the dough or push out the filling.
Prepare your cast-iron skillet or baking pan with oil spray or butter, and arrange the slices, cut size up, in the pan. You want them next to each other, as you can see in the finished photos. The rolls will not touch completely yet, as they will get larger on the next rise and as they bake.
Cover the rolls in the skillet loosely with plastic wrap, and let rise until doubled again - about 60-75 minutes. At this point, if you need to take a break and need to start again the next morning, you can refrigerate the lightly covered pan overnight, about 10-12 hours, where it will slowly rise. If you do this, remove the pan from the refrigerator about 30 minutes before baking (while the oven heats up!), to allow it to come to room temperature.
About 30 minutes before baking, preheat the oven to 350 degrees F. Bake the rolls until they are golden brown, about 25-30 minutes.
While they bake, make the frosting. To do so, combine the butter, powdered sugar, and vanilla in a bowl and mix. Add the milk slowly, until you get the desired consistency. This is a personal preference - some like a runnier frosting, while others like it thicker.
When the rolls are still warm in the pan, drizzle over as much frosting as you desire. Putting the frosting on the warm rolls allows it to slightly soak in, and get even more flavor!
Enjoy warm or let cool and save up to 1-2 days in a covered container stored at room temperature. These are best enjoyed sooner, as they will start to dry out over time!