Preheat the oven to 350 degrees. Grease and line two 8-inch round cake pans with parchment paper.
In a large saucepan over medium-high heat, melt all 2 ½ cups (5 sticks) of butter. Stirring continuously until the milk solids turn light brown. Remove from heat and let cool to room temp.
Stir the cooled browned butter to evenly distribute the browned bits. Remove ¾ cup of the browned butter for use in the cake batter, what remains will be used for the frosting. *See Note.
In a large mixing bowl, beat ¾ cup browned butter and the granulated sugar with a hand mixer until creamy. Add the eggs, next the milk and vanilla, mixing until combined well.
In a small mixing bowl, combine the flour, baking powder, cinnamon, salt, ginger, and nutmeg. Stir with a large spoon to mix well.
Pour the flour mixture into the wet ingredients and use a hand mixer on a low speed to blend the batter. Then turn the speed to high and allow the batter to aerate.
Divide the batter evenly between the two prepared cake pans. Bake for 15-20 minutes, until set in the middle. Remove and allow to cool before turning onto a baking rack. Slice each cake in half evenly.
Cranberry Filling:
Combine all ingredients in a large saucepan over medium heat. Stir frequently. Once the cranberries pop and the mixture begins to reduce and thicken, about 15-20 minutes, remove from the heat and cool to room temp or store covered in the fridge until ready to use.
Browned Butter Frosting:
Whip the remaining browned butter (*see note) and the cream cheese in a medium mixing bowl using a hand mixer. Gradually add in the powdered sugar until it is sweet enough to your taste. Whip at a high speed to aerate the frosting.
Assemble the Cake:
Assemble the cake by beginning with the first layer of sponge on a serving plate, then spoon the Cranberry Filling on top leaving about ½ inch from the edge. Add the second layer of sponge and top it with Browned Butter Frosting. Another layer of sponge and Cranberry filling, then the top layer of sponge and final layer of Browned Butter Frosting gets spread on the top and sides. Decorate as you wish and serve. The cake is best the first day but can be stored covered at room temp for up to 3 days.
Notes
Note: The butter will reduce during the browning process. Typically 1 cup of butter turns into ¾ cup of browned butter.