Chop onion and sauté in a heated and oiled pan over medium high heat for about 3 minutes. Add chopped eggplant and cook until softened, about 5 minutes.
Place in a bowl and in the freezer or fridge to cool. It doesn’t have to get cold, but it can’t be hot.
Preheat the oven to 350˚ and line a baking tray or 2 with silicone baking mats.
Stir cheeses and chicken into the cooled filling, then stir in egg and seasonings.
Lay 1 phyllo sheet on a clean work surface and brush with oil.
Top with a second phyllo sheet and brush again. Cut phyllo sheets lengthwise into 4 long strips.
Place a small dollop ( ~1 ½ tsp) of filling at the top of the oiled strip.
Fold diagonally, then again but in the opposite direction, like a flag. Continue folding down the length of the dough until you are left with a layered triangle.
Repeat this until you have a full baking sheet and brush with just enough oil on the tops to let sesame seeds stick.
Bake on 350° for 10 minutes, then switch the baking sheet's position on the rack and bake another 10 minutes until golden brown.