Remove the phyllo dough from its package several hours ahead and lay out each sheet separately on your kitchen counter or a large surface to dry completely until they become crisp and easy to crumble.

Shred the cheeses and mix them together with the nutmeg in a large bowl.

In another bowl, beat the eggs as you would for an omelet, then add the milk and mix well.

Once the phyllo sheets are dry, crumble half of them into the bottom of a well-buttered 12.5-inch (32 cm) round baking pan or a large rimmed baking sheet.

Spread the cheese mixture evenly over the crumbled phyllo.

Crumble the remaining phyllo sheets over the cheese to cover it completely.

Spoon the egg and milk mixture evenly over the entire pie, making sure every part is covered.

Next, spoon the melted margarine evenly over the top, trying to cover the whole surface.

Sprinkle generously with sesame seeds and let the pie rest for about 15–30 minutes.

If you like, score the top of the pie, then sprinkle a little water over it with your fingers to prevent the sesame seeds from burning. Bake in a preheated oven at 350°F (180°C), using the convection setting, until golden brown on top.