1. Add yeast into the cup of lukewarm water and sprinkle in the teaspoon of sugar. Set aside for about five minutes.
2. Add shortening, 1 cup of sugar, and salt into the hot water in a large bowl or the bowl of a stand mixer fitted with the paddle attachment. Mix to combine, then allow mixture to cool to lukewarm.
3. Add 2 cups of flour and mix until smooth.
4. Add yeast mixture and mix again until smooth.
5. Add in beaten eggs.
6. Stir in cake mix and remainder of flour, a little at a time until no more can be mixed in. Remove the mixer attachment and knead by hand, adding flour until dough does not stick to the bowl (while I did not keep count of total flour used, it was about 3/4 of a 5 pound bag). Remove dough from bowl and knead until dough feels satiny and looks smooth. It shouldn’t be sticking to your countertop at this point, and you should not need any more flour.
7. Cover and let rise for at least 30 minutes.
8. Lightly knead dough and roll out into a long, rectangular shape. The skinnier your rectangle, the smaller your rolls will be, as it will take less turns to roll up all of the dough. The wider the rectangle, the bigger the rolls.
9. Spread the rolled out dough with softened butter, then sprinkle generously with brown sugar, cake mix, cinnamon, and sprinkles.
10. To roll, start with the long end closest to you and roll away from you, keeping the dough rolled as tightly as possible. Pinch along the end to seal.
11. To cut into rolls, use dental floss as opposed to a knife. Wrap the floss around the roll, about 1.5 inches from the end, cross the ends at the top, and pull the ends away from each other until the floss cuts through the dough.
12. Place on well greased pans, cover with a clean dish towel, and let rise in a warm place until doubled in size (or overnight, wrapped with plastic wrap, in the refrigerator).
13. Bake at 425 degrees F for 10 minutes. Reduce heat to 350 degrees F and bake until golden, about 5-7 more minutes, depending on size.
14. While the rolls are baking, make the icing. Whisk together all of the icing ingredients, adjusting milk and powdered sugar amounts to achieve desired consistency.
15. Let rolls cool before frosting to allow for a thick cover like those pictured, or frost while warm for a light glaze.