Preheat the oven to 350°F (180°C).
Trim the ends from the eggplants. Cut each eggplant crosswise into two or three thick pieces.
Use a small knife and spoon to hollow out each piece, leaving approximately ½ inch of flesh around the sides and bottom. Do not cut all the way through.
Finely chop the removed eggplant flesh and set it aside.
Heat 2 tablespoons of olive oil in a large skillet over medium heat. Add the onion and cook for 3–4 minutes, until softened.
Add the garlic and chopped eggplant. Cook for another 4–5 minutes.
Add the ground beef, ¾ teaspoon salt, black pepper, paprika, and cumin. Cook for 7–8 minutes, breaking the meat into small pieces, until browned and cooked through.
Arrange the eggplant cups upright in a baking dish. Season the insides lightly with the remaining salt and fill them with the beef mixture.
Pour ½ cup of water into the bottom of the baking dish. Cover loosely with foil and bake for 15–20 minutes.
Remove the foil and sprinkle the stuffed eggplants with shredded Gouda.
Bake uncovered for another 8–10 minutes, until the cheese has melted and the eggplants are tender. If necessary, bake for an additional 5 minutes.
Cut each pita into eight wedges. Arrange them on a baking sheet, brush lightly with olive oil, and bake for 6–8 minutes, turning once, until crisp.
Spread the yogurt over a shallow plate. Drizzle with extra-virgin olive oil and garnish with paprika, parsley, and Kalamata olives.
Sprinkle the stuffed eggplants with parsley and serve warm with the seasoned yogurt and crispy pita.