Whisk together 2 tablespoons of the sour cream, 1 tablespoon of the oil, 1 tablespoon water, 1 1/2 teaspoons of the curry powder, 1/2 teaspoon of the paprika and 1/4 teaspoon salt in a medium bowl. Add the cauliflower and toss to evenly coat. Cover the bowl and marinate for 30 minutes at room temperature.
Meanwhile, pulse the garlic, ginger, onion and 2 tablespoons water in a food processor until smooth. Heat the remaining 1 tablespoon vegetable oil in a 6-quart Dutch oven or large heavy pot over medium-high heat. Add the onion mixture, garam masala, the remaining 2 1/2 teaspoons curry powder, and the remaining 1 teaspoon paprika. Cook, stirring occasionally, until the mixture starts to stick and brown on the bottom of the pan, about 4 minutes. Add the tomato puree, 1 cup water, the chickpeas and 2 teaspoons salt. Cover partially with a lid and simmer gently until the sauce is slightly reduced and the onion mixture is soft, 10 to 15 minutes.
Meanwhile, preheat the broiler with a rack positioned about 4 inches from the heat source. Line a baking sheet with foil. Arrange the cauliflower in a single layer and broil, tossing halfway through, until the cauliflower is browned and just cooked through, 8 to 10 minutes.
Stir the cauliflower and peas into the sauce and return to a simmer, then remove from heat. Stir in the remaining 6 tablespoons sour cream, the butter and cilantro. Serve the tikka masala in bowls with brown rice and lemon wedges. Garnish with cilantro.
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