Preheat oven to 325°F (170°C). Line bottom of 3 (8-inch) round cake pans with parchment paper. (Do not spray or grease.)
In the bowl of a stand mixer fitted with the whisk attachment, beat egg whites, cream of tartar, and salt at medium-high speed until foamy. Add granulated sugar in a slow, steady stream, beating until glossy, stiff peaks form and stopping to scrape sides of bowl.
In a large bowl, sift together flour and confectioners’ sugar. Gently fold one-third of flour mixture and vanilla bean paste into egg white mixture; gently fold in remaining flour mixture just until combined. Divide meringue among prepared pans (about 2½ cups or 185 grams each). Using a small offset spatula, gently smooth and level tops.
Bake until golden brown and set, 30 to 35 minutes. Turn oven off, and let meringue layers stand in oven with door closed for 2 to 3 hours.
Run an offset spatula around edges of meringue layers to release from pans. Gently invert meringue layers, discarding parchment. Place 1 layer on a serving plate. (See Pro Tip.) Spread 1 cup (180 grams) Chocolate Swiss Meringue Buttercream onto meringue, smoothing with an offset spatula. Repeat with remaining meringue layers and buttercream. Spread remaining buttercream on top and sides of cake. Garnish with sliced almonds, if desired.
Refrigerate for at least 30 minutes before serving or up to 4 hours. If refrigerated for longer than 30 minutes, cake may need to stand at room temperature for a few minutes before serving. Best served same day as made.