Shortcake
Preheat the oven to 350˚F. Place a 10-inch cake pan on parchment; trace and cut out a circle. Grease the pan’s bottom and sides with the tablespoon of butter, press the parchment into the pan, and flip the parchment over, buttered side up. Add 
2 tablespoons of flour and tap to coat the bottom and sides; discard the excess.

Cut the remaining 1 1/2 sticks of butter into small pieces, and melt in a medium saucepan over medium-high heat. Simmer, whisking often to incorporate any solids that sink to the bottom, until the butter is a golden-amber color and smells nutty, 
4 to 6 minutes.
Set the butter aside to cool.

Bring the pot with water back to a simmer over medium-high heat. Whisk the eggs and remaining sugar together in a large heatproof bowl, and place over the pot of water (the bottom of the bowl should not touch the water). Reduce the heat to low and whisk the mixture until it has tripled in volume, 4 to 5 minutes.

Transfer the mixture to the bowl of a stand mixer, and whip on high speed until it is thick, and pale, 2 to 3 minutes.
Meanwhile, sift the remaining 1 cup of flour, the baking powder, and salt together. Reduce the speed of the mixer to low, and slowly drizzle in the warm butter (adding it too quickly will cause the batter to separate), using a rubber spatula to scrape the browned bits into the batter. Alternate adding the dry ingredients and the buttermilk, ending with the last third of the dry mixture, gently mixing until just combined.

Transfer the batter to the prepared cake pan. Bake until the cake sides pull away from the pan and the center resists light pressure, 22 to 26 minutes. Remove from the oven, and let it rest for 10 minutes. Then run a paring knife around the edges of the pan, and invert the cake onto a wire rack to cool.

Stewed Apples
While cake is baking, combine all ingredients for Stewed Apples in a medium saucepan and bring to a boil.
Reduce heat to low and simmer until apples and sogt and sauce is slightly thickened, about 20 minutes.
Set aside. 

Chantilly Cream 
Pour the heavy cream into the bowl of a stand mixer, add the vanilla, and sift in the confectioner’s sugar.
Whip on low speed to combine, and then increase the speed to medium-high.
Whip until medium-stiff peaks form, about 1 1/2 minutes.

Transfer the cake to a plate, and slice into wedges.
Serve topped with stewed apples, sauce, and a dollop of Chantilly Cream, or slice each wedge in half horizontally and sandwich the halves with apples and sauce, then top with cream.