Preheat an oven to 350 F. Grease 6 - 8 oz ramekins with softened butter. Lay them out on a rimmed baking sheet and set aside.
Mix the dry ingredients. In a medium mixing bowl, whisk together the flour, baking powder, salt, and pumpkin pie spice and set aside.
Soak the dates. Place the pitted dates, ginger, baking soda, and tea bag in a small heat-safe bowl. Pour the hot water over the top and let everything steep for 10 minutes. Discard the tea bag, squeezing any liquid out first.
Mix the wet ingredients. Pour the entire date and water mixture into the bowl of a food processor and add the pumpkin puree, eggs, butter, molasses, and brown sugar and pulse until everything is just mixed, but there are still little bits of dates visible.
Mix the batter, distribute, and bake. Pour the wet ingredients into the dry and fold everything together. Evenly distribute the mixture between the 6 ramekins so that they’re about 3/4 full. Bake for 20-25 minutes, until the puddings are puffed in the center. Set them aside.
Make the toffee sauce. While the puddings bake, make the toffee sauce. Melt the butter in a small saucepan over medium heat. Once the butter is hot and foamy, add the brown sugar and heavy cream and whisk well. Continue to cook, while whisking occasionally, for 3-4 minutes, until the sugar has melted and the mixture is smooth. Simmer until the toffee sauce is thick enough to coat the back of a spoon. Remove from the heat and stir in the rum and flaky sea salt to taste.
Pour the sauce over the cakes. Once the puddings are out of the oven, use a skewer to poke holes all over the cake. Drizzle the sauce over the cakes, reserving a bit of the sauce for serving. Sprinkle the tops of the cakes with a bit of flaky sea salt. Let the cakes cool until they’re slightly warm. Top with soft whipped cream or ice cream.