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To prepare the puddings, preheat the oven to 350 degrees F. Brush the inside of six 6-ounce heat-proof custard cups or ramekins with the melted butter.
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Invert the custard cups on a baking sheet and refrigerate until the butter sets.
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In a medium bowl, whisk together the flour, baking soda, salt, cinnamon, nutmeg, and coriander.
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In the bowl of a stand mixer fitted with the paddle attachment (or in a large bowl with a handheld mixer), beat the 8 tablespoons butter and the cane sugar on high speed until the mixture is light and fluffy.
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Add the eggs one at a time, followed by the yolk and the vanilla, beating well and scraping down the side of the bowl with a rubber spatula after each addition.
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Beat in the pumpkin puree and scrape down the bowl.
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Add the flour mixture in thirds, alternating with the buttermilk, beating each time only until the batter is smooth.
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Use an ice cream scoop or large spoon to carefully divide the batter among the custard cups, taking care to keep the rims clean.
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Gently tap each cup to remove any air bubbles.
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In a lidded baking dish or Dutch oven large enough to hold the custard cups with at least 1/2 inch of space between them, place a folded kitchen towel (to hold the cups steady).
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Arrange the custard cups in the dish.
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Pour enough very hot tap water into the baking dish to come halfway up the sides of the cups.
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Cover the baking dish tightly with the lid.
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Bake until a toothpick inserted into the center of a pudding comes out clean and the top springs back when gently pressed, 30 to 40 minutes.
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Remove the lid and let the puddings cool in the water bath for 20 minutes.
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Meanwhile, prepare the hard sauce.
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In a medium bowl, beat the butter with an electric mixer set to high speed until fluffy.
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Reduce the speed to low and add the confectioners' sugar.
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When the sugar is incorporated, increase the speed to high, and beat until the mixture is light and fluffy.
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Fold in the nutmeg and rum with a rubber spatula; you should have about 1/2 cup.
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Use within 1 hour or transfer to a bowl, cover, and refrigerate for up to 1 week.
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Allow the sauce to come to room temperature before serving.
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The puddings can be served warm or at room temperature.
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If serving directly in the custard cups, serve at once or let cool on a wire rack.
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If unmolding, to serve the puddings warm as soon as they come out of the water, run a thin knife around the inside of each ramekin to loosen the puddings, then invert into a serving plate.
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To serve at room temperature, place the ramekins on a wire rack until the puddings cool before inverting them onto serving plates.
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Top each serving with about 1 tablespoon of the hard sauce and a large shard of brittle.
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Generously butter a rimmed baking sheet or line it with a silicone baking mat.
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In a large skillet, cook the pumpkin seeds over medium heat, stirring often, until they are lightly toasted, about 3 minutes.
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Transfer to a plate to cool.
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In a large, heavy, deep saucepan, combine the cane sugar, corn syrup, 1/4 cup water, and 2 tablespoons butter.
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Cook over medium heat, stirring with a long-handled wooden spoon until the sugar dissolves.
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Increase the heat to medium high, and bring the mixture to a boil.
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Let the mixture boil without stirring until it turns deep amber, 8 to 12 minutes.
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Remove the pan from the heat and carefully stir in the baking soda, vanilla, and salt.
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The mixture will bubble vigorously and expand in the pan.
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Immediately stir in the pumpkin seeds and pour onto the prepared baking sheet.
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Use a heat-proof spatula to gently but quickly spread the brittle into a thin, even layer.
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Let the brittle cool to room temperature.
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Run an offset spatula under the brittle to help loosen it, or gently twist the pan.
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Break the brittle into shards.
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Store in an airtight container at room temperature for up to 2 weeks.