Pour vegetable oil into a heavy based saucepan over a medium heat, bring the oil to 170°C. If you don't have a thermometer, test the temperature of the oil by dropping in one of your donut holes - if it immediately starts to bubble and rise to the surface, your oil is hot enough.
While the oil is heating, cut donut shapes out of your thawed puff pastry. Use a large, round cookie cutter and a much smaller one to remove the "donut hole". I got 6 donut shapes per sheet of puff pastry.
As soon as the oil has reached the correct temperature, gently lower in your first donut. It will start to puff up and brown.
Once the bottom of the donut is golden brown, turn it over with a slotted spoon and let it brown on the other side before quickly removing it from the oil and placing on paper towel to drain.
Repeat this process with the remaining donuts (and donut holes!) until all are golden brown. Be careful the oil doesn't get too hot as they may start to burn.
Put the Nutella in a small piping bag and pipe a thick line of Nutella around the top of half the cooled Fauxnuts.
Gently sandwich the remaining Fauxnuts on top of each one.
Dust the top of each Fauxnut with icing sugar.