Preheat the oven to 400 degrees F (200 degrees C). Spray a 9x13-inch glass baking dish with cooking spray.
Combine orange juice, olive oil, garlic, mustard, lemon juice, oregano, salt, pepper, cumin, and turmeric in a food processor; pulse to get a thick sauce.
Place potatoes in the prepared pan and pour sauce over top. Toss to coat.
Bake, covered, in the preheated oven for 40 minutes. Uncover and continue to bake until potatoes are tender, about 20 minutes more. Top with fresh thyme.