Open the can of crescent rolls and lay the 4 small rectangles next to each other to form a large rectangle. Press the seams together and smooth out all of the perforations in the dough.
Use a butter knife to spread 1 Tbsp butter on the entire dough rectangle (go ahead and use a little more if you'd like).
Mix 1/3 cup brown sugar with the cinnamon until well combined. Spread the cinnamon/sugar filling on the buttered dough, covering all of the dough with the filling except for about a 1 inch row across the top. Doing this makes the dough seal better when you roll it up.
Starting at the bottom, roll the dough up. Cut the dough into twelve 1-inch cinnamon rolls. (I like to start by making one cut in the middle of the roll, and then placing one cut in the center of each half, dividing the dough into quarters. Then divide each of those quarters into thirds. Doing it this way helps you to space your cuts evenly across the dough and ensures that you end up with 12 equally sized rolls every time!)
Grease 12 cups in a mini muffin pan and then place a little pat of butter in the bottom of each cup. I used 2 Tbsp of butter and divided it into 12 little sections. Use the extra 2 Tbsp of brown sugar and divide it evenly amongst the twelve cups, sprinkling a little on top of each pat of butter. Doing this makes the bottoms of the rolls taste even better and it also makes the rolls easier to remove from the pan when they are done baking.
Place each roll into the prepared muffin tin and bake at 375 for about 10-12 minutes, until golden brown on top.
While the cinnamon rolls are baking, mix all the ingredients together with an electric mixer until smooth. As soon as the rolls are out of the oven, frost each one while they are still in the pan. Let cool for a few minutes and then remove from pan - they are definitely best warm!