Preheat the grill. Brush the bread with oil on both sides and season with salt and pepper. Grill bread on both sides until lightly golden brown. Remove the bread to a platter and let sit at room temperature to get slightly hard.
Meanwhile, whisk together 1 cup olive oil, lemon juice, and dill in a medium bowl. Season, to taste, with salt and pepper. Fold the cucumber, tomatoes, onion, and feta into the oil mixture and let stand at room temperature for 30 minutes. Spoon the mixture over the bread. Garnish with additional dill and drizzle with chili oil, if desired. Serve immediately.