Add the cheeses and stir until well-mixed. Turn off the heat.
Add the dill and the eggs, and season with pepper as needed.
Put about half to 2/3 of the Filo on the bottom of the pan, and brush with melted butter after each sheet. If the sheets are too large for the pan, let them come up the sides of the pan.
Spread the filling evenly over the filo.
Cover with the remaining sheets and brush with butter again.
Cut into serving-size pieces before baking, and trim the edges to make it neat.
Bake at 350 for 45 minutes to one hour, until golden.
Allow to cool somewhat before serving.
Notes
It is very important to cut the pie into serving pieces before you bake it. The Fillo gets too crispy to cut neatly afterward.
I get Dodonis feta at Bahnan's in Worcester. You can probably also get it in Watertown. Or in Greece.