About an hour before starting, separate egg whites from yolks. Cover yolks with cold water and refrigerate. Let egg whites warm to room temperature in a measuring cup or small bowl.
Preheat the oven to 375°F conventional. Set rack to the middle shelf.
Sift cake flour and powdered sugar together. Set aside.
Beat egg whites with cream of tartar in the bowl of a stand mixer or with a hand mixer until foamy and the cream of tartar is evenly distributed.
With the mixer on high speed, beat in granulated sugar 2 tablespoons at a time until the meringue is stiff and glossy. Add the vanilla, almond extract, and salt with the last addition of sugar.
Remove the bowl from the mixer. Sprinkle the flour-sugar mixture over the meringue ¼ cup at a time, folding just until the flour-sugar mixture disappears after each addition. Do not overfold.
Push the batter into an ungreased 10x4-inch tube pan. Run a metal spatula gently through the batter or tap the pan lightly on the counter to settle it and eliminate air pockets.
Bake 30 to 40 minutes, until the top cracks feel dry and spring back when lightly touched. A tester inserted into a crack should come out with only a few clinging crumbs.
Immediately invert the pan over a bottle and cool completely, at least 1 hour.
To unmold, run a flat offset spatula around the outer edge and a thin knife or cake tester around the center tube. Invert onto a cooling rack, lift off the pan, and turn the cake right side up.
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Notes
Yield: One 10-inch tube pan, 16 servings. Doneness Cue: Top cracks feel dry to the touch and the surface springs back when lightly pressed. A tester inserted into a crack comes out with only a few clinging crumbs. Storage: Wrap cooled cake in plastic wrap or store in an airtight container at room temperature for up to a week. Do not refrigerate: the sugar will pull moisture from the air inside the fridge and the cake will turn soft and gummy. Make Ahead: Freeze the fully cooled cake for up to 3 months. Unwrap and thaw completely at room temperature before serving.