This recipe was inspired by a suggestion in an ad on the back of the November 1933 issue of Better Homes & Gardens. The recipes are adapted from All About Home Baking (1933), p. 36 and The New Joy of Cooking (1953), p. 704 and p. 757.
For the cake: Preheat the oven to 350 degrees Fahrenheit. Grease an 8" square cake tin and line the bottom with parchment. Set aside.
Cream the butter and sugar in a large mixing bowl. Beat in the egg.
Alternate between mixing in the flour (about 1/2 cup at a time) and milk (about 1/4 cup at a time). Beat well to combine, but don't over mix. Add the baking powder, salt, ginger and mixed spice with the last addition of flour.
Pour batter into the prepared tin, smooth out and bake in the middle of the oven about 40 minutes, or until a cake tester comes out clean.
Cool cake in the tin 10 minutes, then leave on a rack to cool completely before frosting.
To make the cream cheese frosting: Stir together the cream cheese and milk, then sift in the powdered sugar, a bit at a time. Stirring after each addition. Add the 1 1/2 tablespoons lemon zest and brandy and stir to combine. Spread over the top of the cooled cake. Refrigerate to set the icing.
To make the lemon sauce: Combine the sugar, cornstarch and water in a heavy-bottomed saucepan and cook, stirring, over medium heat until mixture thickens. It should be slightly thicker than you want your finished sauce to be. This will take 10 to 15 minutes.
Remove from the heat and stir in butter, 1/2 teaspoon lemon zest, lemon juice and salt. Leave sauce to cool to just above room temperature or cooler, so it won't melt your cream cheese frosting. Serve sauce alongside slices of cake.