Thin grilled naan creates atastypocket for a veggie burgerwith an Indian twist.
Stir together yogurt, lime juice, and a pinch of salt in a small bowl. Refrigerate sauce, covered, until ready to use.
Heat oil in a medium skillet over medium heat. Add onion, garlic, 1 1/2 teaspoons salt, and the pepper. Cook, stirring, until onion is translucent, about 5 minutes. Stir in curry powder and ginger; cook 3 seconds more. Add carrot, beets, and zucchini; cook, stirring often, until vegetables are just tender, about 2 minutes. Let cool 10 minutes.
Pulse rice, chickpeas, and half of the vegetable mixture in a food processor until it forms a coarse paste. Transfer to a medium bowl. Stir in remaining vegetable mixture and the breadcrumbs. Season with salt and pepper.
Shape into 6 oval patties (about 4 inches long). Refrigerate, covered, until cold, about 30 minutes (or up to 3 hours).
Preheat grill to medium (if using a charcoal grill, coals are ready when you can hold your hand 5 inches above grill for just 5 to 6 seconds). Brush grill and burgers with oil. Grill burgers, flipping once, until charred and heated through, 3 to 4 minutes per side.
Grill bread, flipping once, until softened and lightly charred. Serve burgers on bread; top with tomato and reserved yogurt sauce. Garnish with parsley.