Preheat the oven to 400°F (200°C). Slice the eggplants in half lengthwise, score the flesh in a diamond pattern without cutting through the skin, brush with 2 tablespoons of olive oil, and roast on a baking sheet for 20 minutes until soft and lightly browned.

While the eggplants roast, heat 1 tablespoon of olive oil in a skillet over medium heat. Sauté the sliced onions and minced garlic for 8 to 10 minutes until caramelized and sweet. Stir in the diced tomatoes, cumin, salt, and pepper, then simmer for 10 minutes until the mixture thickens into a rich compote.

Prepare the tzatziki by combining the Greek yogurt, grated and squeezed cucumber, lemon juice, and one minced garlic clove in a small bowl. Season with salt and a drizzle of olive oil, then refrigerate until ready to serve.

Season the lamb chops generously with the Greek seasoning, salt, and pepper on all sides. Preheat a grill pan or outdoor BBQ to medium-high heat, brush with the remaining oil, and sear the lamb chops for 4 to 5 minutes per side for medium-rare, or until a beautiful charred crust forms.

Remove the roasted eggplants from the oven and gently press down the centers to create a well. Stuff each eggplant half generously with the warm tomato-onion mixture, then return them to the oven for an additional 10 minutes to meld the flavors.

Plate the warm stuffed eggplants alongside the grilled lamb chops. Spoon the chilled tzatziki over the lamb or serve it on the side, garnishing with fresh mint leaves for a bright, aromatic finish.