Combine milk, brown sugar, butter, salt and vanilla in a sauce pan, and place it over a medium heat. Do not boil. Turn it off.
Place the cornstarch in a bowl and add half of the milk to make a fine paste, then pour other half and mix thoroughly and return to heat. Lower the heat, whisking often,, until the mixture comes thick and shiny. Pour the pudding into a serving bowl and sprinkle brown sugar on top. Let it cool and then cover the bowl with a plastic wrap tightly and refrigerate until cold.
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