Preheat the oven to 350 degrees.
In a large bowl, whisk together the pumpkin, eggs, milk, and vanilla. In another bowl, stir together the brown sugar, cornstarch, spices, and salt and sift into the pumpkin mixture. Stir the batter until combined well and pour into four 3/4-cup custard cups.
Place the cups in a 9 X 11-inch baking pan and add enough warm water to come halfway up the sides of the cups. Bake for 50 minutes, or until set and browned lightly. Transfer the custards to a wire rack to cool.