In a large bowl (or a stand mixer), add the milk, yeast, and sugar, and stir to combine. Let the mixture rest for 2 minutes.
Add the eggs, oil, and salt, and mix to combine.
Add 3 cups of flour and mix well; continue mixing for 2 minutes.
Continue adding the rest of the flour until a soft dough forms, and mix until well combined.
Turn the dough out onto a lightly floured surface, and knead, adding flour as needed, until a smooth dough forms.
Shape into a ball, and return the to bowl you mixed it in. Cover with plastic wrap or a clean dish towel, and let the dough rest for 30 minutes. It won't rise much, just a bit.
After 30 minutes, remove the dough from the bowl onto a lightly floured work surface. Roll it into a rectangle that is about 24 inches wide and around 18 inches tall (it can be a bit taller; it's a rough rectangle).
In a medium bowl ,add the melted butter, brown sugar, and cinnamon and stir to combine well.
Spread the sugar mixture all over the rolled dough, leaving a 1 inch gap of dough along the top with no cinnamon mixture.
Roll the dough up starting at the bottom (which is 24 inches wide) up to the top where there's a bit of dough without filling.
Mark the dough doll roll by making a small slit in the middle, then divide the middle into two more pieces (you are now up to 4 pieces), and then divide each of those 4 quarters into 3 more pieces. This is to divide the dough evenly into 12 pieces. Each line should be about 2 inches apart.
Use a serrated knife to cut the rolls where you made your marks.
Place the cut rolls, cut side down, in a parchment lined or greased large 17x11-inch baking dish, 3 rolls wide and 4 rolls down.
Cover with plastic wrap or a clean dish towel, and let rest for 30 minutes.
While the rolls are resting, preheat the oven to 350 degrees F.
After the 30 minute rest, remove the towel or the plastic wrap, and place in the oven. Bake for 20 minutes or until golden-brown.
While the rolls are cooking, make the icing.
Add the melted butter to a medium bowl. Add the vanilla and the powdered sugar, and mix well to get out all the lumps. It helps if the butter is warm or even a bit hot when you mix in the sugar. Add enough cream or milk, and stir to combine until you get a medium-thin consistency, about as thick as toothpaste.
When the rolls come out of the oven, let them cool for 5 minutes and then frost warm and serve.
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Notes
A 9x13-inch and a 17x11 inch baking dish both work great for this recipe, you can use two 9-inch cake pans and put 6 rolls in each pan.
Use a serrated knife for cutting the rolls to avoid squishing the dough. Marking the dough first helps achieve even-sized rolls for uniform baking.
Spread the cinnamon-sugar filling evenly over the dough, leaving a small border. This prevents the filling from spilling out during rolling and ensures each roll has a consistent, delicious flavor.
TO MAKE THESE THE NIGHT BEFORE: Make the dough as directed but don't let it rise in the bowl. Skip the first rise and roll out the dough and make the cinnamon rolls as directed and place them in your prepared pan. Cover the pan well with plastic wrap and refrigerate right away. Keep in the fridge overnight or up to 18 or so hours. When you are ready to bake, remove the rolls from the fridge while your oven preheats. When the oven is hot cook the rolls according to the directions, adding a little time as needed to cook them until golden brown. I normally bake them 5-10 minutes longer. Frost and serve.