Add the oil to a 10-inch skillet over medium-high heat. Use a thermometer to properly gauge the temperature (325°F to 340°F is the target range). While the oil is heating, prepare the donuts.
Unroll the can of cinnamon rolls and separate each cinnamon roll, being careful to keep the cinnamon rolls themselves from unrolling. Once unrolled, slightly press down each of the cinnamon rolls. Set the icing aside.
Press down the center of the cinnamon roll by using a large decorator's tip (for cake decorating), an apple corer, or even a clean water bottle cap to cut out the center. Set the donut hole aside. Repeat removing the remaining cinnamon roll centers.
Pinch or press the seams on the outer edge of the cinnamon roll together (it will pull apart if it is not sealed).
Place a cooling rack over a baking sheet lined with paper towels to place the cooked cinnamon roll donuts on to drain the excess oil.
Once the oil reaches the desired temperature, carefully add 3 to 4 of the cinnamon rolls. Cook for 1 to 2 minutes per side, until golden. Use a slotted metal spoon to carefully turn the cinnamon roll over to continue cooking. Keep a close eye on the temperature to ensure you don’t burn the donuts. Place the cooked cinnamon roll donuts onto the prepared baking sheet to drain excess oil. Repeat the process for the remaining donuts and the donut holes (my favorite part).
When all the donuts have been cooked, open the icing packet and, using a knife or offset spatula, spread the icing over the donuts and donut holes.