Preheat the oven to 200°C (400°F).
Toss the diced eggplant and cauliflower florets in half of the olive oil and spread them out on a baking tray. Roast in the oven for 25-30 minutes, or until golden and tender, stirring midway.
While the vegetables roast, season the chicken breast with garlic, dried basil, salt, and pepper. Heat the remaining olive oil in a skillet over medium heat and cook the chicken for about 6-7 minutes per side, or until cooked through and no longer pink in the center. Let it rest for 10 minutes before slicing.
In a mixing bowl, combine the roasted eggplant, cauliflower, chopped tomatoes, and arugula. Drizzle with balsamic vinegar and toss gently to combine.
To serve, layer the salad mixture in a serving bowl, top with sliced chicken, and garnish with fresh parsley. Serve with a generous spoon of yogurt on the side.