Defrost the phyllo dough and return the remainder to the freezer. Butter a cookie sheet. Melt the butter and remove from the heat.
Preheat the oven to 375 degrees F.
Mix the feta and cream cheese with the egg, parsley, and dill and set aside.
Layout one sheet of phyllo dough on a counter.
(Keep the remaining dough covered with a slightly damp towel to prevent its drying out.) Brush the sheet of dough with some melted butter. Cut it the short way into 5 strips, about 3x10 inches each. Place 1-1/2 teaspoons of the filling at one end of each strip. Roll the strips into cylinders about 1/2 inch in diameter. Continue until all of the dough has been cut, filled, and rolled.
Arrange 2 to 3 cylinder per person on the cookie sheet and brush them with more butter. (Freeze the rest of the cylinders, unbaked, for use at another time.) Bake for about 10 minutes, or until the cylinders are well browned and very flaky.
Bureks, frozen unbaked, can go directly from the freezer into a preheated 375-degree F oven to make an instant hors d'oeuvre.