Prepare the Eggplant: In a bowl, whisk together the eggs, milk, flour, and baking powder until smooth. Season the batter with salt and black pepper.

Dip each eggplant slice into the batter, ensuring each slice is well coated.

Fry the Eggplant: Heat vegetable fat in a large skillet over medium heat.

Fry the battered eggplant slices until golden brown and crispy, about 2-3 minutes per side. Remove from the skillet and drain on paper towels.

Make the Vegetable Filling: In the same skillet, add a little more vegetable fat if needed and sauté the grated carrot, sliced mushrooms, and chopped bell pepper until they are soft and lightly browned, about 5-7 minutes.

Add the chopped tomato and chives, cooking for another 2 minutes until the tomatoes are just soft.

Turn off the heat and stir in the grated cheese until it melts slightly.

Prepare the Sauce: In a small bowl, combine the yogurt, mayonnaise, ketchup, minced garlic, and chopped dill. Mix well until the sauce is smooth and creamy.

Assemble and Serve: Place a few eggplant slices on each plate. Top with a generous amount of the vegetable filling.

Drizzle the creamy sauce over the top or serve it on the side for dipping.