Preheat oven to 325°F.
Line two baking sheets with parchment paper.
In a medium bowl, whisk together: cake flour, baking powder, salt and set aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat the butter and sugar on medium speed for 5 full minutes, until very pale, fluffy, and almost mousse-like.
Mix in: egg whites, heavy cream, sour cream, vanilla, almond extract and beat until completely smooth, scraping down the bowl as needed.
Using a 2-tablespoon cookie scoop, portion the dough onto the prepared baking sheets, leaving about 2½ inches between each cookie.
Lightly dampen your fingertips and gently flatten each mound into a thick disc about ½ inch tall.
Bake for 12–14 minutes, or until the cookies are puffed and set.
The tops should remain pale, and only the very bottoms should show the slightest hint of golden color.
They may look slightly underbaked in the center...that's exactly what you want.
As soon as the cookies come out of the oven, loosely tent the baking sheet with aluminum foil for 8–10 minutes.
The trapped steam gently finishes baking the cookies while keeping them exceptionally soft and moist.
Transfer to a wire rack and cool completely.