Take pita and slice each in half. Place in a 300°Foven for 8-10 minutes. Remove from oven when pita is warm and starting to get crispy. Wrap in foil to keep warm and set aside.
While piat are in the oven, place the butter in a large skillet on medium-high heat.
Slice onion in half then cut 1/4 slices. Cut slices in half once more and place in hot butter. Sauté until onions become tender, around 5 minutes.
Whisk eggs and milk together. Add pepper to eggs then pour entire mixture on top of the onions.
Scramble the eggs until they are just beginning to come together and hold the scrambled egg shape.
Throw the feta cheese on top of the eggs and gently mix inches You want the feta to retain it's chunks so don't mix them in so much that they melt into the eggs. (Our family always preferred to cook our eggs well done, however if you like your eggs on the softer side you will want to add the feta cheese a minute or two earlier).
When the eggs are cooked to your preference, taste and adjust seasoning. Depending on the type of feta used, more salt may be needed and additional pepper can be mixed in as well.
Take the warmed pita bread and lightly butter the inside. Stuff each half with an 1/8th of the mixture.