Preheat oven to 350°F (180°C). Spray an 8-inch spring form pan with baking spray.
In a medium bowl, combine apples. Microwave on high until apples are softened but not translucent, about 2 minutes. Let cool; strain excess liquid.
In the bowl of a stand mixer fitted with the paddle attachment, beat egg and 2 tbsp sugar at medium speed until pale in colour, about 2 minutes. Stir in melted butter, brandy, and vanilla paste.
In a medium bowl, whisk together flours, baking powder, salt, and remaining 1 cup sugar. Gradually add flour mixture to egg mixture alternately with milk, beginning and ending with flour mixture, beating just until combined after each addition.
In a large bowl, whisk together 1 cup batter and egg yolks. Stir in apples until combined, reserving ¼ cup apples. Spread egg yolk batter into prepared pan. Top with remaining batter, smoothing with an offset spatula. Press reserved ¼ cup apples into top of batter, and sprinkle with almonds.
Place spring form pan on a rimmed baking sheet to catch any drips. Bake in bottom third of oven for 30 minutes. Raise spring form pan to middle of oven, and bake until a wooden skewer inserted in center comes out clean, about 35 minutes more, loosely covering with foil to prevent excess browning, if necessary. Let cool in pan for 15 minutes. Run a knife around edges of cake to loosen before removing from pan. Let cool completely on base of pan before serving.Inspired by BakeFromScratch recipe
