Preheat your oven to 325°F (165°C). Line a 9x13-inch baking pan with parchment paper, leaving a slight overhang on the edges for easy removal.

In a large bowl, cream together the softened butter and 1/2 cup sugar until light and fluffy, about 2-3 minutes. Beat in the egg yolks one at a time, followed by the vanilla extract.

In a separate bowl, whisk together the flour and baking powder. Gradually add the dry ingredients to the butter mixture, alternating with the milk, and mix until just combined. Spread this thin layer of cake batter evenly into the bottom of the prepared pan.

In a clean glass or metal bowl, whip the egg whites until soft peaks form. Gradually add the 1 cup of sugar, one tablespoon at a time, whipping continuously until stiff, glossy peaks form.

Carefully spread the meringue evenly over the unbaked cake batter in the pan. Sprinkle the sliced almonds evenly across the top of the meringue.

Bake for 35-40 minutes, or until the meringue is beautifully golden brown and crisp to the touch. Remove from the oven and let the cake cool completely in the pan.

While the cake cools, prepare the filling. In a medium bowl, whip the heavy cream and vanilla bean paste until stiff peaks form. Gently fold the whipped cream into the vanilla custard until smooth and well incorporated.

Once the cake is completely cool, use the parchment overhang to lift it out of the pan. Carefully cut the cake in half crosswise to create two equal rectangles. Place one half, meringue side down, onto a serving platter.

Spread the creamy vanilla filling evenly over the bottom cake layer. Top with the second cake layer, meringue side up, and refrigerate for at least 1 hour before slicing to allow the layers to set perfectly for serving.