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1
Put the butter in a 3 quart heavy saucepan over medium heat. Once the butter stops foaming, and you see orangey brown specks start to appear, stir gently with a wooden spoon. After a minute or two, when the specks are nut brown and the butter smells nice and toasty, sprinkle 1/4 cup of sugar over the butter and stir to combine. (It will clump up a little, but don't worry!)
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2
Switch to a whisk, and cook the butter and sugar, whisking all the time, until the sugar has melted and the mixture becomes a smooth, rich brown caramel, about 5 minutes. (Early on, the butter and sugar will separate, and the butter will pool around the edges of the sugar, but never fear! Once the sugar has fully melted, the two will start to come together again, and you'll have a nice smooth caramel.)
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3
When the caramel is a rich nut brown and starts to smoke, remove the pan from the heat and quickly and carefully whisk in the creme fraiche and about 1/2 a cup of the milk. Don't worry if the mixture bubbles up when you do this - it'll settle down again quickly. (This step cools off the caramel and keeps it from cooking further.) Return the pan to the heat and whisk in the rest of the milk, the remaining 3 tablespoons of sugar, the vanilla seeds and the salt. If the caramel seizes a little, just keep whisking until the mixture becomes smooth again.
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4
Switch back to the wooden spoon and stir in the rice. Turn up the heat and bring the mixture to a boil. Reduce the heat so that the milk is simmering steadily and cook the rice pudding uncovered for about 25 minutes, stirring frequently to make sure nothing sticks to the bottom of the pan, especially towards the end. The rice should be tender but not mushy, and the pudding should thicken but still be quite loose - remember that it will thicken a lot more while it's cooling. Transfer the pudding to a container, cover and refrigerate until cold. Serve in individual bowls with a dollop of creme fraiche.
