In bowl of stand mixer, measure gluten free flour by stirring the flour, scooping into measuring cup, and leveling off with a knife.
Add yeast, then salt on the opposite side of the bowl.
Add prepared pudding, butter, eggs, and milk and mix on low-medium speed until dough is smooth. This should take 1-2 minutes. Don't mix on high.
At this point, your dough should be quite sticky - see the attached video. If it is too think and not sticky enough, add milk a tablespoon at a time until it's the right consistency. If it is too wet and sticky, add flour a tablespoon at a time. Keep in mind that your dough needs to be quite sticky - much too sticky to handle. In the next step, you will coat the outside of your dough with flour so you can roll it out, but you want the dough itself to be nice and wet so that it will rise.
Prepare cinnamon sugar filling by combining the butter, sugars, and cinnamon. Mix with a fork or pastry blender until combined and crumbly.
Now it's time to roll out the dough. If you have a silpat or baking mat, that will make nice, non-stick surface to roll out your dough. A counter-top will work fine too.
Sprinkle a tablespoon or two of gluten free flour or starch on your surface, put your dough on top, then sprinkle another tablespoon of flour or starch over it.
You want your dough to remain nice and wet/sticky because gluten free dough soaks up a lot of moisture when it's baking. So try not to work the flour/starch into your dough, just coat it so you can roll it out.
Once you have dusted your surface and dough, roll it out to about 16" by 11". If the rolling pin sticks to the dough, sprinkle a little more flour on.
Sprinkle the cinnamon sugar filling over your dough and press it down gently.
Starting at the longer end, roll the dough, trying to keep your roll as tight as possible. Once it is in a nice log, press down on the edges to seal them.
Now it's time to slice. There are many methods, feel free to use your favorite. I have a dough scraper that I LOVE and use all the time (there's a link to it below). It does a great job and slicing the cinnamon rolls and is quick and easy. Some use floss, and that works well too.
You're going to make a slice right in the middle, then cut each of those halves in half so you have 4 pieces. Next, cut each of those pieces into 3 slices. Now you'll have 12 cinnamon rolls of equal sizes :)
Lightly grease a 9x13 baking pan and arrange your cinnamon rolls in 4 rows of 3.
Cover your pan with plastic wrap or a light towel.
Allow the cinnamon rolls to rise in a warm location. I heat my oven to 120 degrees F, turn off the oven, put the pan in, and close the door.
Let the rolls double in size. check them after about 20 minutes, sometimes that's all it takes.
Once the dough has risen to double its size, or almost double, preheat your oven to 350 degrees F. Remove the pan from the oven before preheating.
Once the oven is preheated, put the rolls in and bake for 25-30 minutes. Mine take the full 30 minutes. Your rolls should start to brown on top and be done in the middle. Once they're done, remove from the oven to cool in the pan.
Prepare the frosting by creaming together the butter and cream cheese until smooth. Add powdered sugar and vanilla and mix until creamy.
Frost the cinnamon rolls and serve! They are great warm, and best served the day you make them. If you have leftovers, store in an airtight container and warm them briefly in the microwave before serving.