Preheat the oven to 375°F. Butter 2 baking sheets.
Squeeze the shredded zucchini in a clean dish towel to remove as much of the moisture as possible.
In a large bowl, combine zucchini, shredded Cooper® Sharp White cheese, pesto sauce, salt, and pepper. Set aside.
Lay out 1 phyllo sheet lengthwise on a work surface. (Keep the others loosely covered with a damp towel.) Brush the dough with melted butter.
Top with another layer of dough. With a sharp knife, cut the phyllo dough horizontally into 3 evenly sized pieces. Place a heaping tablespoon of the zucchini mixture in the lower right corner of each strip and fold upward and over on the diagonal to form a triangular shape.
Continue folding until you reach the end of the strip and have an enclosed triangular pastry.
Place all 3 triangles on a prepared baking sheet.
Continue these steps with the remaining phyllo sheets and filling. Brush the tops of the pastries with melted butter.
Bake in the oven for about 20 minutes or until golden brown.