Preheat the oven to 480°F/250°C. Line a large baking tray with parchment paper (depending on the size of your oven, you may need two trays).
Roast the aubergines and tomatoes. In a medium bowl, place the aubergine rounds and tomatoes with the olive oil, salt and black pepper. Mix well and spread out on the baking tray(s). Roast in the oven for 25-30 minutes, until golden-brown and completely soft. Remove from the oven and set aside to cool.
Make the black garlic dressing. Place the black garlic coves in the small bowl of a food processor with olive oil, 2 tablespoons of yogurt, lemon juice and a pinch of salt. Blitz until smooth to form a rough paste. Transfer it to a medium bowl and mix in the rest of the yogurt. Set the dressing in the refrigerator until ready for serving.
To serve. Butter both sides of each slice of toast and grill both sides on a grill pan or skillet until lightly toasted. Cut each slice of toast in half. Evenly distribute the roasted aubergine and tomatoes on the toasts. Evenly distribute on the feta cheese and dill. Carefully spoon on the black garlic dressing over each slice of toast.