Preheat oven to 300°F (150°C). Line two baking sheets with parchment paper.
In a large bowl, whisk egg whites with cream of tartar until foamy. Gradually add granulated sugar, one tablespoon at a time, until stiff glossy peaks form.
Fold in vanilla and almond extracts gently to preserve volume.
In another bowl, sift together almond meal and powdered sugar. Gently fold into the meringue until uniform without deflating.
Pipe or spread three 8-inch circles onto the prepared sheets, smoothing tops for even layers.
Bake for 25 minutes, rotate sheets, then bake 15–20 more minutes until edges are golden and centers feel slightly soft. Cool completely on racks.
Whip cold cream with powdered sugar and vanilla until medium peaks form. Layer whipped cream between cooled meringues, then chill at least 2 hours before slicing.
Notes
I found that sifting the almond meal twice yields a finer crumb.Sealing cooled layers in parchment overnight prevents them from softening.Use a gentle folding motion when combining nuts with meringue to keep the mixture airy.