Step 1

Heat the oven to 375ºF with a rack in the middle position. Coat a 9-inch springform pan with butter, dust evenly with flour, then tap out the excess.

Step 2

Melt the butter in a 12-inch skillet over medium-high. Cook, swirling the pan frequently until the milk solids at the bottom are golden brown and the butter has a nutty aroma, 1 to 3 minutes. Pour into a small heatproof bowl without scraping out the skillet. ** see notesStir the allspice into the butter and set aside.

Step 3

Add all of the apples, 2 tablespoons of sugar, and salt to the still-hot skillet and set over medium-high. Cook, stirring occasionally, until all moisture released by the apples has evaporated and the slices are beginning to brown for 12 to 15 minutes. Add the brandy and cook until evaporated 30 to 60 seconds. Transfer to a large plate, spread in an even layer and refrigerate uncovered until cool to the touch, 15 to 20 minutes.

Step 4

In a small bowl, whisk together the flour and baking powder. In a large bowl, whisk together the eggs, vanilla, and 9 tablespoons of the remaining sugar. Gradually whisk in the browned butter. Add the flour mixture and stir with a rubber spatula until smooth; the batter will be very thick. Add the cooled apples and fold until evenly coated with batter.Transfer to the prepared pan, spread in an even layer and sprinkle with the remaining 1 tablespoon sugar.

Step 5

Bake until deeply browned, 35 to 40 minutes. Let cool completely in the pan on a wire rack for about 2 hours. Lightly dust with Confectioners Sugar. Run a knife around the inside of the pan and remove the sides before slicing.