Salt and Pepper to taste or Cajun spice instead, no more than 2 tsps.
Peel and thinly slice your potatoes and cut the half an onion into long slices (Or mince if you prefer smaller onions) combine in a bowl and then transfer to a standard-sized cast-iron or nonstick skillet.
Add 1 cup of olive oil and bring to a boil.
Fry until the potato starts to get crispy on the edges and either breaks apart easily or can be pierced easily by a fork.
Turn off the heat and remove any excess oil leaving about 1 or two tbsp. in the pan with the potatoes and onions.
Beat your eggs with Cajun spice and minced green onions and add to the pan with the fire on and the oil hot. Cook until the edges are crispy (You can also lift the omelet with a spatula to check underneath, you don't want to leave it on too long or it will burn.) Then take a flat plate larger than the pan width and place it upside down on the skillet. Lift the skillet and flip the omelet onto the plate, and then slide the uncooked side back into the pan being careful not to spill.
Check the bottom of the omelet again for crispy doneness and then slide it onto a serving dish. Let chill in the fridge if you desire it cold (which is traditional) or eat it hot.
You can also save it for later, it makes a great picnic snack and keeps for at least a week in the fridge. Enjoy!