Old-Fashioned Apple Cake with Brown Sugar Frosting

Preheat the oven to 325°F. Lightly grease a 9" x 13" pan or line with a parchment paper sling. Alternatively, grease or two 8" round pans or line with parchment.

To make the cake: In a large bowl or the bowl of a stand mixer fitted with the flat beater attachment, mix all of the ingredients except the apples, boiled cider, and nuts. As soon as the mixture comes together and becomes uniformly crumbly, stop mixing; you don't want it to turn into a cohesive mass.

Add the apples, boiled cider, and nuts, and mix until the apples release some of their juice and the stiff mixture becomes a thick, creamy batter, somewhere between cookie dough and brownie batter in consistency. Don't worry if the mixture doesn't immediately loosen up; this will take about 3 minutes at low speed in a stand mixer.

Spread the batter in the prepared pan(s), smoothing it with a rubber spatula or damp fingers.

Bake the cake for 45 minutes for a 9" x 13" pan or for 38 minutes for two 8" round pans, checking the cake(s) after about 30 minutes and covering with foil if the top is browning quickly. The cake is done when a toothpick or paring knife inserted into the center comes out clean or with just a few wet crumbs clinging to it. The temperature of the center of the cake will be about 205°F when measured with a digital thermometer.

Remove the cake from the oven and place it on a rack to cool a bit while you make the frosting.

To make the frosting: Sift the confectioners' sugar into a bowl or onto a piece of parchment or wax paper; set it aside. (This guarantees lump-free frosting.)

In a medium saucepan over medium heat, melt the butter. Stir in the brown sugar and salt and cook, stirring, until the sugar starts to melt and the mixture becomes fairly smooth, about 3 to 4 minutes. While you may still notice a bit of grittiness from the sugar, you shouldn't see any melted butter pooled atop the sugar. Add the milk and boiled cider, and bring to a boil.

Remove the syrup from the heat and pour it into a medium-sized mixing bowl (large enough to accommodate the confectioners' sugar). Let the syrup cool in the bowl for 10 minutes.

Pour the confectioners' sugar into the warm syrup in the bowl, then add the vanilla extract. Whisk until everything is thoroughly combined. You need to work fast here; the frosting stiffens up quickly as it cools.

Pour the warm frosting onto the cake(s), spreading it over the entire surface.

Serving and storage information: Cut the cake with a sharp serrated knife for the cleanest slices. Store any leftover apple cake, covered, at room temperature for several days; freeze for longer storage.