In a food processor blend well all pesto ingredients. Pesto may be made 3 days ahead and chilled, surface covered with plastic wrap.
Lightly brush a large baking sheet with some butter and put 1 sheet phyllo on butter. Lightly brush phyllo with some remaining butter and sprinkle with 1 tablespoon Parmesan. Put another sheet phyllo over cheese, pressing firmly so that it adheres to bottom layer. Butter, sprinkle with cheese, and layer remaining phyllo in same manner, ending with a sheet of phyllo. Lightly brush top sheet with remaining butter. Fold in all sides 1/4 inch, pressing to top sheet, and fold up a 1/4-inch border, crimping corners.
Spread pesto and phyllo crust and sprinkle with feta.
Bake pizza in middle of oven until crust is golden, about 15 minutes.