For the filling, bring water to a boil in a large Dutch oven. Add the spinach, escarole and chicory. Cover and cook, stirring occasionally, until greens are wilted, about 5 minutes. Drain greens in a colander, pressing out excess liquid.

Melt the butter in a large skillet over medium-high heat. Add onions and cook until softened, 3 minutes. Add cooked greens, parsley, dill, pepper, salt and nutmeg; cook 2 minutes more. Cool greens mixture then add goat cheese, feta and egg; mix well.

Arrange oven rack in lower third of oven. Place a cookie sheet on rack. Heat oven to 425 degree F. Brush a 9-inch metal or glass pie plate with melted butter. Place 1 phyllo sheet in pie plate, letting sides overhang. Brush lightly with butter to 1 inch beyond edge of plate. Layer and butter 7 more sheets of phyllo. Spoon in greens filling. Layer and butter remaining 8 phyllo sheets on top, then trim edges of phyllo with scissors to form a 1-inch overhang. Tuck overhang under and flute edge. Place on the cookie sheet on rack and bake 25 to 30 minutes. Cover edges of pie with foil. Reduce oven temperature to 375 degrees F. and bake 25 to 30 minutes more, until pie is golden and center is puffed. Cool on wire rack 5 minutes before cutting. Makes 8 servings.