Finely dice onion and parsley leaves. Shred or mince cheese in a food processor.
Whisk an egg with a tablespoon of just-melted butter (you don't want to boil your egg).
Stir all ingredients together (onion, parsley, jack cheese, butter and egg.)
Unroll a defrosted package of phyllo dough. Cut the entire stack of phyllo dough sheets in half, length-wise, to make strips about 3-4" wide.
Cover one stack with saran wrap and a wet towel, to keep moist.
Butter one strip of phyllo dough with a pastry brush. Add another strip of phyllo dough to the top, and brush that layer with butter. Add a third strip of phyllo dough to the top, and brush the final layer with butter. You should have three sheets of phyllo dough, buttered in between.
Add 2 tablespoons of filling in the bottom corner of your phyllo dough. Take the bottom corner of all sheets and make a diagonal fold to the other side. Continue folding using a flag roll method.
Brush the tops and bottoms of all the boreks with butter before baking and place on a cookie sheet. (You won't need to grease the cookie sheet.)
Bake in the middle rack at 375 degree Fahrenheit for 15-18 minutes or until lightly browned on both sides. Serve immediately.