In a bowl place the flour, pudding, sugar, and eggs. Knead until all ingredients are combined and a sticky, doughy batter is formed. Cover with a kitchen towel and let rest for 15-20 minutes.
Heat 6 cups of canola oil in a 6-quart stock pot, covered, over medium heat. When dough is ready, uncover oil and raise heat to high.
Scoop out a tablespoon of batter and drop in oil. (Don't make doughnuts too big, they expand and you want them to cook through.) You should be able to fry 6 or so doughnuts at a time.
When the beignets are browned on one side use slotted spoon to turn them over and fry until the enire doughnut is golden.
Remove beignets and let cool and drain on paper towel lined plates. Repeat with remaining batter.
Fill a squeeze bottle, flavor injector, or syringe with jelly, jam, custard etc. and inject a little into each doughnut. Or leave plain.
Sprinkle each doughnut with confectioner's sugar or roll in confectioner's sugar or shake 3 at a time in a paper bag with confectioner's sugar.
If needed you can make your own self-rising flour by mixing 8 cups of flour with 1 Tablespoon of salt and 5 Tablespoons of double acting baking powder. Blend and store in an air tight container labeled "SELF-RISING".