Prepare the eggplants by peeling strips on their skin. Keep the top on. Cut a slit in each eggplant with going all the way through.
Fill a large bowl with cold water and add 1 tsp salt to the water. Stir and place the eggplants in the salt water. Soak them for 30 minutes.
Meanwhile, heat 2 tbsp olive oil in a pan over medium heat and saute onion until translucent. Add in minced garlic and cook until golden brown.
Add in ground beef and brown it completely. Add diced green pepper and tomato to the ground beef mixture and cook for a few minutes.
Add in tomato paste, salt and pepper to the filling and mix well.
Discard the salt water and gently squeeze the eggplants. Dry them using a paper towel.
Heat 1/4 cup vegetable oil in a pan over medium heat and fry the eggplants on all sides until they're soft and brown.
Preheat the oven to 350F.
Place them on a paper towel to absorb the excess oil.
Place the fried eggplants in a baking dish and stuff them with the ground beef mixture.
Make the sauce by mixing the tomato paste in water and spoon it over the eggplants and into the dish. Bake in the oven for 30 minutes until the eggplants are completely cooked and soft.
Serve warm with white rice and cacik.