Place the egg yolks and eggs in a good-size bowl. Beat them gently.
Slowly pour in the whipping cream, mixing it into the eggs as you pour.
Gradually add the pumpkin puree, stirring continually.
In a small bowl, stir together 1⁄3 cup sugar, cinnamon, ginger, and cloves. Stir those dry ingredients into the liquid mixture gradually.
Grease a 1 1⁄2- or 2-quart baking dish that fits into your 6- or 7-quart oval slow cooker crock. Fill the baking dish with the pumpkin mixture. Place it in the crock.
Pour water around the baking dish in the crock until it comes halfway up the sides of the dish. Be careful not to get any water in the filled dish.
Cover the cooker. Cook on Low 2 to 3 hours, or until the brûlée is set but not hard. It should be a little soft in the center.
Using oven mitts, remove the baking dish from the crock and set it on a wire rack to cool to room temperature.
Then cover and refrigerate for 2 to 8 hours.
Before serving, let the brûlée stand at room temperature for 30 minutes.
To caramelize the sugar for the topping, heat remaining 1 cup sugar in an 8-inch heavy skillet over medium-high until it begins to melt. Shake the skillet rather than stirring the sugar to heat it evenly. When the sugar starts to melt, reduce the heat to low. Cook it for 3 to 5 minutes more, or until it’s golden, stirring it as needed with a wooden spoon so it doesn’t burn.
Quickly drizzle the caramelized sugar over the brûlée. Serve it immediately.
You can prepare the brûlée in individual 6-ounce ramekins, too, but you’ll need two 6-quart slow cookers and 6 ramekins. Fit 3 filled ramekins into each cooker. Follow Steps 6 through 12 above to complete the dessert.
Stock up on 3 or 4 cans of pure canned pumpkin in the autumn in case the store doesn’t have any when pumpkin is out of season.