Preheat an oven to 350 degrees F (175 degrees C). Grease a baking sheet with shortening. Place the phyllo sheets between two pieces of waxed paper and top with a damp cloth.
Place a large piece of waxed paper on a flat surface. Place one sheet of the phyllo dough on the waxed paper; use a pastry brush to spread melted butter over the sheet to coat in a thin layer, starting on the edges and working your way to the center. Place a second sheet of phyllo dough atop and repeat the brushing with butter; top the second sheet with a third sheet and again brush with butter. Repeat the process with the remaining three sheets and butter so you have two stacks of three sheets of buttered phyllo dough.
Arrange about 1/4 cup of the mozzarella cheese along one edge of each of the phyllo dough stacks. Spread 3/4 cup of the corn chowder along side each line of mozzarella cheese. Roll each of your phyllo dough stacks into a long roll with the fillings in the center; brush the tops of each roll with melted butter. Place the rolls on the prepared baking sheet.
Bake in the preheated oven until golden brown, 25 to 30 minutes. Cut into bite sized pieces to serve.