In a small bowl, combine the cream cheese, lightly beaten egg, Parmesan, and salt. Stir to combine. Spoon mixture into a plastic zip-top bag. Set aside. To use as a pastry bag, cut corner off bag to make a 1/4-inch diameter opening.
Lay out thawed phyllo dough. Working quickly to keep dough from drying out: brush top sheet with melted butter, pipe cheese filling along long edge of phyllo 1/2-inch from each end. Fold over ends to seal in filling and roll up straw. Repeat with remaining sheets of phyllo and place on a baking sheet. Bake until golden, about 10 minutes.