Preheat the oven to 325 degrees F (165 degrees C).
Whisk egg yolks and brown sugar together in a large bowl. Stir in heavy cream, pumpkin puree, allspice, cinnamon, nutmeg, and salt.
Divide pumpkin mixture between seven (5-inch) ramekins about 1/2 inch from the top.
Place the ramekins in a baking dish and fill with the baking dish hot water to reach halfway up the sides of the ramekins.
Bake in preheated oven until just set, 30 to 35 minutes.
Remove ramekins and refrigerate until completely cool, at least 2 hours.
Sprinkle about 1 tablespoon of sugar onto each creme brulee. Melt the sugar with a chef's torch until crisp and dark brown, 1 to 2 minutes. Allow to cool before serving.
