Preheat the oven to 350ºF (177ºC).
Line with parchment paper two 8-inch round cake pans, then grease parchment with softened butter and coat with flour. Set aside.
In a small bowl, whisk together the cake flour, baking powder, and salt. Set aside.
To the bowl of a food processor, add the sugar, eggs, vanilla, and almond extracts, processing until combined, about 10 seconds.
With the food processor running, add melted butter in a steady stream until incorporated.
Transfer this sugar mixture to a large bowl.
Sift flour mixture over sugar mixture in 3 additions, whisking to combine after each addition until few streaks of flour remain.
Continue to gently whisk the batter until almost no lumps remain.
Divide cake batter evenly among the prepared cake pans.
Bake until toothpick inserted in centers comes out clean, 24 to 28 minutes, rotating pans halfway through baking.
Let cakes cool in pans on a wire rack for 10 minutes.
Run a paring knife around the edges of the pans to loosen, if needed.
Remove cakes from pans, discarding the parchment paper, and let cool completely on rack, about 2 hours.
While the cakes cool, prepare the cherry whipped cream.