Preheat oven to 300°F. Combine heavy cream, 1⁄3 cup sugar, vanilla extract, cinnamon, cloves, and ginger in a medium saucepan and bring to a boil. Remove from heat. Reserve.
Combine egg yolks and remaining 1⁄3 cup sugar together in medium bowl. Add 1⁄3 of the hot cream to egg mixture, whisking constantly. Add the egg mixture back into the remaining hot cream, whisking constantly. Gently whisk in pumpkin.
Pour pumpkin mixture evenly into 5 – 4 ounce ramekins. Bake in a water bath in the center of oven until slightly set in the center – approximately 40 minutes. Remove from oven and let cool to room temperature. Cool completely in the refrigerator before serving.
Preheat oven to broil. Place 1 tablespoon brown sugar on top of each custard in an even thin layer. Place the ramekins under the broiler until the sugar is caramelized to a golden brown. Watch carefully as color will change very quickly under broiler. Serve immediately.