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1
In a small saucepan, combine the milk with 4 of the cardamom pods, the vanilla bean and seeds, the cinnamon stick and 1/4 cup plus 2 tablespoons of sugar.
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2
Bring to a simmer, stirring until the sugar dissolves.
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3
Remove from the heat and let stand for 45 minutes.
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4
Strain the infused milk into a bowl and discard the solids.
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5
Meanwhile, in a medium saucepan, combine the strawberries, framboise, lime zest and the remaining 1/4 cup of sugar and 2 cardamom pods and let stand for 10 minutes.
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6
Cook over high heat, stirring occasionally, until the berries are softened, 4 to 5 minutes.
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7
Let cool slightly.
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8
Discard the lime zest and cardamom pods.
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9
In a large saucepan, melt the butter.
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10
Add the grits and cook over high heat, stirring until heated through, about 5 minutes.
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11
Gradually whisk in the warm water.
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12
Reduce the heat to moderately low and cook, stirring with a wooden spoon every 2 to 3 minutes, until the water has been absorbed and the grits are thickened, about 20 minutes.
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13
Whisk in the infused milk until smooth.
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14
Cook, stirring frequently with a wooden spoon until the grits are thickened, about 30 minutes longer.
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15
Pour the grits into a shallow 5- to 6-cup baking dish and let cool for 10 minutes.
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16
Preheat the broiler and position a rack 8 inches from the heat.
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17
Sprinkle the brown sugar over the grits and lightly rub it into an even layer.
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18
Broil the grits until the sugar melts and caramelizes, about 5 minutes, shifting the dish as necessary for even browning.
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19
Alternatively, use a propane torch to caramelize the sugar.
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20
Spoon the grits into shallow bowls and top with a scoop of ice cream.
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21
Spoon the strawberry compote on the side.