Preheat the oven to 350° and set a rack in the center. Grease the bottom and sides of an 8-inch springform pan lightly with butter, then line the bottom with parchment paper. Set aside.
In a small saucepan, add 3⁄4 cup water and the chopped dates; bring to a simmer. Remove the pan from the heat and transfer the dates and liquid to a bowl; refrigerate until cool.
Meanwhile, in a medium bowl, add the flour, baking powder, baking soda, cinnamon, nutmeg, and salt; whisk briefly to combine.
In a stand mixer fitted with the paddle attachment, or in a large bowl using an electric mixer, add the 8 tablespoons butter, the brown sugar, and granulated sugar; beat on medium-high speed until fluffy, scraping down the bowl as needed, 3-4 minutes. With the mixer on low speed, add the eggs and coffee or vanilla extract; beat on low speed until combined. With the mixer on its lowest speed, add a third of the flour and the dates to the mixture; mix on low until just combined. Add half of the milk; mix to incorporate. Follow another third of the flour mixture, then the remaining milk, then the final third of the flour mixture, mixing on low speed each time to just incorporate.
Transfer the batter to the prepared pan, distributing evenly and smoothing the top. Bake until the pudding has risen and a cake tester or thin skewer inserted almost all the way through the center comes out with no gooey bits remaining, 60-65 minutes. Remove the pan from the oven and transfer to a cooling rack; let the pudding cool in the pan for a few minutes.
Meanwhile, make the toffee sauce. In a medium saucepan, add the granulated sugar, brown sugar, 4 tablespoons water, and the salt; cook over medium-high heat for 5 minutes, stirring or swirling the pan occasionally. Add the butter, then the ¾ cup cream, lemon zest, and coffee extract, stirring until the butter has melted and the mixture is smooth.
Using a long skewer, poke deep holes all over the pudding (the pudding should still be in the pan), separating them by around ½ inch to 1 inch. Spoon about half of the caramel onto the top of the pudding, spreading it around with the back of the spoon. Let the pudding cool completely in the pan, then cover the pan with a sheet of plastic wrap and let the pudding stand at room temperature for 12 to 24 hours. Reserve the remaining toffee sauce in the refrigerator.
To serve, whip the remaining heavy cream to soft peaks.
In a small saucepan over medium-low heat, rewarm the caramel sauce until runny. Carefully remove the pudding from its pan and transfer to a serving platter or cake stand if desired. Drizzle with most of the remaining sauce to taste.
Serve the pudding sliced into wedges with the ice cream and any leftover sauce for topping.