Preheat the oven to 200°F.
To a measuring cup, add the milk and sugar. Warm the milk/sugar mixture up in the microwave for about 25-30 seconds, then give it a stir and make sure it is only lukewarm -- if it’s hot (rather than lukewarm), allow it to cool for a minute or two. Stir in the yeast and place the cup on top of the preheating oven.
Using a baking scale, measure out the dough ingredients (flour, eggs, avocado oil, cane sugar, and salt) and add them to the bowl of your stand mixer.
Take a look at the yeast mixture -- if it has started to bubble and froth, your yeast is alive and ready to use. Once bubbly and frothy, pour the yeast mixture into the bowl with the dough ingredients.
Attach the dough hook to the stand mixer and mix starting on low and working your way up to medium-speed. Keep the mixer on for about 7 minutes -- after this time, you should end up with a smooth, tacky, and sticky dough.
Prepare a large glass bowl by coating it with oil. Using a spatula, scrape the dough out of the mixing bowl into the prepared glass bowl, and cover it with saran wrap. Turn off the oven and open the door, then place the bowl into the warm oven and set a timer for 10 minutes, keeping the oven door open a crack for those 10 minutes. After the 10 minutes is up, close the oven door and set the timer for 50 minutes. You’ll know that the dough is done rising when it doubles in size (see tips and tricks below if you are struggling to get a good rise). Remove the dough from the oven and turn the oven back on to preheat it to 375°F.
Place a large sheet of parchment paper on your work surface, and sprinkle a good amount of flour across the paper. Add your cinnamon roll dough to the center by flipping the bowl upside down, then sprinkle more flour on top of the dough -- use just enough to prevent sticking (try not to overdo it). Press the dough out so that it is 14 inches by 12 inches.
Spread the softened butter across the surface of the dough, leaving ½ of an inch without butter around the edges. Then, sprinkle the brown sugar and cinnamon over the buttered surface.
Using either your hands (this will give you a tighter roll with more layers) or the parchment paper as a guide, start rolling the dough. To begin, roll up a little at a time, moving back and forth across the whole width as you go. After you do your first roll, give the dough a tiny tug to make sure it’s nice and tight, and then continue the process. After each new roll, give the dough another little tug to keep the roll nice and tight. When you reach the end, roll the dough so that it is seam-side down.
Using a sharp knife, trim off the end pieces if they are less thick/uniform. Using your ruler and knife, mark every 1 ½ inches on the roll (this will give you 9 same-size buns). Using a sharp knife, bench scraper, or floss, gently cut each roll.
Place the two tablespoons of melted butter into your pan, then add the cinnamon rolls to the pan, spacing them a ½-inch apart if possible. Brush 2 tablespoons of heavy cream or milk on the tops and sides of the rolls, then cover the pan with saran wrap or a kitchen towel and place it on top of the warm oven until the buns double in size (this should take 30-60 minutes). Once doubled in size, remove the saran wrap or kitchen towel and brush them a second time with the remaining 2 tablespoons of milk or cream.
Place the cinnamon rolls into the 375°F oven, and bake for 20-23 minutes. Keep an eye on the rolls and cover them with tinfoil for the last few minutes if they brown too quickly. When finished, they should be golden brown and you should see no raw pieces on the top of the buns.
While the buns bake, make your cream cheese frosting. Add all of the frosting ingredients to a medium bowl or the bowl of your stand mixer and beat on medium-high until fluffy and smooth.
Spread the frosting over the hot buns as soon as you remove them from the oven. Enjoy!