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Melt butter in a saucepan and then remove it from the heat. Brush the bottom of an 8 to 9 inch square baking pan with butter.
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Use several sheets of filo to line the bottom of the baking pan with a layer to filo. Arrange the filo in the pan so that it goes up the sides of the pan and hangs over the edges of the pan.You will fold the filo "overhang" over your pie at the end of your preparation. Brush the filo with butter.
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Use about 1/3 of the filo sheets to partially fill the lined baking pan with filo. This is where you rip or scrunch the sheets into little "rags." You can just wad them up in your hand and place them in the pan. Once you have placed the filo rags into the pan, sprinkle half of the feta over the filo. Then, sprinkle 1 T. of the Parmesan over the feta. Sprinkle the feta/Parmesan cheeses with some fresh thyme leaves. Pour about 1/3 of the melted butter over the filo/cheese filling.
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Using another 1/3 of the ripped or scrunched filo sheets, fill the baking pan with another layer of the filo. Add feta, Parmesan and fresh thyme as you did to the last layer. Pour more butter over this layer.
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Finally, using larger pieces of the remaining filo, make one last layer of the pie adding the remaining feta, Parmesan and fresh thyme.
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Fold the filo that is overhanging the sides of your pan over themselves around the edge of the pan. Pour the remaining butter over the top. (I used a pastry brush to help me distribute the butter.)
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Use a sharp knife point to make two cuts down and two cuts across the filo-packed tin. You want to create 9 squares. This can get a bit messy, but the filo pie is very forgiving when baked.
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Beat eggs and milk together and pour over the contents of the baking pan. Sprinkle the remaining thyme leaves and the sesame seeds on the top of the pie. Let the pie sit on your counter for at least 30 minutes at this point. If you want to wait for a couple of hours to bake this, cover the pie and store it in your refrigerator.
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Bake the pie for 30 minutes at 350 degrees F in a heated oven. Your pie is done when the pastry is golden-brown and puffed and the inside is set. Let the baked pie sit on your counter for about 10 minutes to cool and solidify. Drizzle a generous amount of honey over the top of the pie, cut into servings using a serrated knife and serve warm with extra honey for your guests to add to their portions if they like. Garnish with fresh thyme sprigs.