Melt the butter in a small saucepan, then take it off the heat.
Line a 20cm/8in square cake tin with a layer of filo, making sure it comes up the sides; you will need to use more than one sheet. Then pour 1 tablespoon of melted butter over the pastry.
Using one third of the remaining filo sheets, tear and scrunch the sheets up and drop them loosely in the tin. Then crumble in half the feta, sprinkle with 1 teaspoon of Parmesan and just under ½ teaspoon of thyme leaves (or ¼ teaspoon of dried thyme) and pour a third of the remaining melted butter over the top.
Repeat, so that you use up all but a little of the butter and a small amount of thyme. For the last layer, you can use larger pieces of filo “rags” (as it’s the lid), filling the tin a little more tightly, but still scrunching them.
Fold the edges of overhanging filo over themselves, and pour the remaining butter on top. Using the sharp point of a knife, make 2 cuts down and 2 cuts across into the filo-packed tin, from edge to edge to create 9 sections. It’s important that you don’t use a blunt knife, as you don’t want to drag the filo or press down on it.
Beat the eggs with the milk, then pour over the contents of the tin. Sprinkle the last bit of thyme along with the sesame seeds on top. Let it stand for at least 30 minutes in a cool place before baking. If 2 hours is easier for your timetable, then put it in the fridge. And you can do this in advance (see top recipe tips).
Heat the oven to 200C/180C Fan/Gas 6, and bake the pie for 30 minutes. When it’s ready, the pastry will be golden-brown and puffed up, and the inside set. Let it stand for 10 minutes, then spoon 1 tablespoon of the honey over the top.
Cut into slices or slabs – using a serrated bread knife and sawing action to prevent squishing the filo on top too much, then pushing the knife down to cut through. Serve the pie directly from the tin and put the jar of honey, with a spoon in it (or you can pour it into a jug) on the table for people to add extra as they eat.