Preheat oven to 350 F.
Unroll dough on lightly greased cookie sheet; press seams together to form 12- by 4-inch rectangle.
Lightly press oregano into feta cheese. Place feta cheese, oregano-side up, in center of dough. Bring edges of dough up over feta cheese; press edges together to seal, completely enclosing feta cheese. Brush with egg.
Bake at 350 degrees for 20 minutes or until lightly browned.