Heat the oven to 400 F with rack in the center. Line a shallow baking sheet (10×15 or 11×17) with parchment paper or foil (shiny side down). If using foil, spray with vegetable oil cooking spray to prevent vegetables from sticking.

In a large bowl, stir to combine the oil, cumin, turmeric, salt, and garlic. Add the chicken, turning to coat, and then transfer smooth side up to the baking sheet. Add the vegetables to the bowl and toss in the remaining spiced oil, then distribute them around the chicken pieces on the baking sheet. Season with freshly ground pepper.

Roast the chicken and vegetables for 25 minutes. Sprinkle the grapes over the vegetables and roast about 5 minutes more, until the juices run clear when the chicken is pierced with the tip of a small sharp knife. (Note: for softer roasted grapes, add them to the pan earlier.)