Melt the butter over medium heat in a large skillet and add the green onions. Sauté until fragrant, about 5 minutes.
Meanwhile, whisk the eggs and milk in a bowl. Add to the butter and onions in the skillet and begin to scramble.
Halfway through being done, add the rice and begin to scramble them all together until the eggs are fully cooked. This should take 6 to 7 minutes to make sure the rest of the egg is cooked and the rice is fully heated.
Season to taste with salt and pepper or Cajun seasoning, if using. You can also add extra butter if you like at the end; that’s fine too! Serve and enjoy!