Preheat the oven at 350 degrees Fahrenheit (180 Celsius).
Heat the oil over moderate heat in a large pan.
Add the chopped onion sautéing until soft about 3 minutes.
Add the garlic and sauté another 30 seconds.
Add the eggplant and sauté for 4-5 minutes.
Add the tomato and continue cooking until soft for about another 4-5 minutes. Add parsley, sugar, salt and pepper to taste.
Once warmed up, remove from heat, empty in a bowl and let the mixture cool down.
In another bowl beat the egg, add the crumbled feta and the yogurt and mix well. Add to the eggplant mixture once it is cool. Stir. Add the breadcrumbs and mix. At this point you can place the mixture in the refrigerator and use later (you can leave overnight).
When you are ready to make the turnovers take out the phyllo (it should be defrosted). Spread out 1 sheet of phyllo (keep the rest covered), brush a small amount of olive oil. Cut the sheet in 4 strips lengthwise (or 3 for larger pieces).
Place on the top corner of each strip about 1 ½ teaspoon of the eggplant mixture. Start folding in a small triangle (see here). Continue until you use the whole mixture. Place eggplant pies on a lightly greased pan, brush them with a bit of olive oil and sprinkle with sesame seeds. Bake until golden, about 25 minutes.
Let them cool and enjoy warm or at room temperature.
