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Whisk the tandoori paste, lemon juice, and 1/4 cup of yogurt in a 13 x 9 x 2-inch (32 x 22 x 5cm) baking dish to blend.
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Using a large sharp knife, score the skin of the game hen halves. Sprinkle the hen halves with salt.
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Add the hen halves to the tandoori marinade and rub the marinade all over them.
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Cover and refrigerate for 1 hour.
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Add the shrimp to the same dish and rub all over with the marinade.
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Continue to marinate the hen halves and shrimp for 45 minutes.
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Preheat the oven to 500°F / 260°C.
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Line a large heavy baking sheet with foil.
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Place a wire rack on the baking sheet. Set the hen halves skin side up on the rack.
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Roast the hen halves until they are almost cooked through, about 20 minutes.
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Arrange the shrimp on the rack alongside the hen halves and roast until the hen halves and shrimp are cooked through and golden brown, about 10 minutes longer.
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Meanwhile, stir the cucumber and remaining 1 cup of yogurt together in a bowl.
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Season the raita to taste with salt and pepper and reserve.
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Sprinkle the lettuce on a platter, if desired. Arrange the hen halves and shrimp atop the lettuce.
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Garnish with lemon wedges and cilantro sprigs.
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Serve with the raita, mango chutney and naan bread.