Preheat the grill to high heat. Drizzle the vegetables with olive oil and season with salt and pepper. Grill the vegetables, flipping once, until tender and grill marks appear. Remove from the grill and set aside.
To make the dressing, in a small bowl or jar, whisk together the olive oil, red wine vinegar, lemon juice, Dijon mustard, garlic, oregano, salt, and black pepper. Set aside.
To assemble the bowls, roughly chop the grilled vegetables. Divide the farro between 4 bowls and top each bowl with the grilled vegetables, chickpeas, cucumber, tomatoes, Kalamata olives, and feta cheese. Garnish with herbs and season with salt and pepper, to taste. Drizzle with dressing and serve with tzatziki and pita chips or pita bread, if desired.