Preheat your oven to 400°F (200°C). Line a baking sheet with parchment paper for easy cleanup.
Wash the eggplants and bell peppers. Pat them dry and cut the eggplants into 1/2-inch thick slices, and the bell peppers into large strips, discarding the seeds and stems.
Arrange the eggplant slices and bell pepper strips on the prepared baking sheet. Drizzle with olive oil and toss gently to coat. Ensure the vegetables are in a single layer for even roasting.
Roast the vegetables in the preheated oven for about 30 minutes, or until they are tender and the edges begin to brown. Halfway through the cooking time, flip the vegetables to ensure they roast evenly.
While the vegetables are roasting, prepare the yogurt dressing. In a medium bowl, combine the Greek yogurt, minced garlic, lemon juice, red wine vinegar, salt, and black pepper. Whisk until smooth and creamy.
Once the vegetables are done, remove them from the oven and let them cool slightly. Then, coarsely chop the roasted vegetables into bite-sized pieces.
In a large serving bowl, combine the chopped roasted vegetables with the yogurt dressing. Toss until the vegetables are well coated.
Garnish with chopped parsley and mint before serving. The salad can be served warm or chilled, according to preference.