Make the turkey: Preheat oven to 450°F with rack in lower third position. Place turkey on a large baking sheet, and let stand until room temperature, about 1 hour.

Whisk together yogurt, cilantro, cream cheese, ginger-garlic paste, lemon juice, tandoori masala, salt, garam masala, kasoori methi, and black pepper in a medium bowl until well combined and smooth. Gently slide your fingers under the skin of the breast and thighs of turkey to loosen. Generously rub yogurt marinade under the skin and inside the cavity using your fingers. Brush a thin layer of the marinade over the breast and thighs; reserve the remaining marinade. Stuff turkey cavity with lemon halves, and tie the bird’s legs together tightly using kitchen twine (see Notes from the Food & Wine Test Kitchen)

Combine 2 cups water, onion, and carrot in a large roasting pan; fit a V-shaped rack into the pan. Place turkey on rack, breast side up.

Roast turkey, rotating pan occasionally, until browned in spots, about 1 hour. Brush turkey with some of the reserved yogurt marinade, and quickly return to oven. Reduce oven temperature to 350°F, and continue to roast until an instant-read thermometer inserted into inner thigh registers 165°F, 20 to 30 minutes. (If turkey starts getting too dark, tent loosely with aluminum foil.) Transfer roast turkey to a carving board, and let rest for 30 minutes. Meanwhile, pour turkey drippings through a fine wire-mesh strainer into a medium bowl. Discard solids, and set liquid aside for gravy. (You should have about 3/4 cup drippings. If you do not have enough, use chicken stock to make up the difference.)

Make the gravy: Melt ghee in a medium saucepan over medium. Add cumin seeds and tandoori masala. Cook, stirring often, until fragrant and cumin begins to crackle, about 1 minute and 30 seconds. Whisk in cornstarch until smooth and no lumps remain. Gradually whisk in chicken stock and reserved turkey drippings until mixture is smooth and lump-free. Bring to a simmer over medium. Reduce heat to medium-low; cook, stirring occasionally, until thick enough to coat the back of a spoon, about 3 minutes. Pour through a fine wire-mesh strainer into a dish or gravy boat.

Serve turkey with gravy, chaat masala, melted ghee, and lemon wedges.