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Preheat the grill or a grill pan over medium heat.
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Make the curry: Warm the oil in a large sauté pan over medium heat. Add the garlic and sauté until fragrant but not browned, 1 to 2 minutes. Stir in the turmeric and cook until fragrant, 1 to 2 minutes. Add the cream, paprika, and chile powder, bring to a simmer, and slowly reduce, allowing the flavors to develop and stirring frequently, 15 to 20 minutes. Adjust the seasoning with salt and lemon juice. Keep warm.
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Make the raisin chutney: Plump the raisins and currants in boiling water for 30 seconds. Drain. In a mixing bowl, combine the raisins, currants, almonds, cilantro, and chutney.
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Toss the broccoli in the canola oil and 1 teaspoon salt. Grill, turning frequently, until tender, blackened, and crispy around the edges, about 12 minutes. Arrange on a platter and top with the turmeric curry and raisin chutney. Drizzle with the curry oil and serve.