Heat oven to 350º.

In a medium-size saucepan over medium heat, melt ⅓ cup butter and whisk in flour to form a paste. Cook, whisking a minute or so. Add milk slowly, whisking to prevent lumps. Add a few grates of nutmeg. Lower heat and cook, whisking often until thickened. Remove sauce from heat and cool to room temperature.

In a medium-size mixing bowl, mash feta into a crumbly paste. Stir in white sauce. Add beaten eggs, a few tablespoons at a time, mixing until smooth. Stir in parsley; season with a few pinches of pepper and a few grates of nutmeg.

Lay phyllo on a clean work surface and cover with a slightly damp kitchen towel. Take one sheet from the pile, keeping the rest covered. (You can use torn sheets; patch them together and brush with melted butter.)

Line a buttered 9x13-inch baking dish with 5 layers of phyllo dough, brushing each layer with melted butter.

Spread cheese mixture over pastry. Cover with remaining phyllo, buttering each layer. Top with last phyllo sheet; fold edges over surface and brush with butter.

Score top sheets into 3-inch squares. Bake until pastry is golden-brown, about 45 minutes. Cool slightly; then cut into squares and serve warm.