Making a great doughnut is just as important to me as it is to make a great choux pastry. A light as air brioche doughnut is one of the best things there is.
I used to submerge my doughnuts completely when I fried them, but this would take away one of the visual quality aspects that I have seen, which is the white ring around the middle section. That is a sign of a well made, well proofed and well fried doughnut.
It should also not be greasy. Doughnuts become greasy when they are fried in oil that is too cold or are not proofed properly (usually when they are overproofed); they tend to suck the oil right in. When the oil is at the correct temperature (350 F for large doughnuts / 365 F for smaller ones) it seems to seal the outside crust and the heat just expands the dough through steam, creating a fried doughnut that is light as air.