Preheat the oven to 350º. Place nuts in a single layer on a rimmed baking sheet; toast until golden and aromatic, about 8 minutes. Shake the pan halfway through baking to make sure the nuts toast evenly. Remove from oven; cool. Reduce oven temperature to 200º. Line two 11-by-17-inch baking sheets with parchment; set aside.
In the bowl of an electric mixer, combine egg whites and sugar. Place bowl over a pan of simmering water. Whisk until sugar dissolves and mixture is warm, 3 minutes.
Transfer the bowl to the mixer fitted with the whisk attachment. Starting on low speed and gradually increasing to high, whip mixture until stiff, glossy peaks form, about 5 minutes. Add vanilla, and mix to combine. Remove bowl from mixer, and fold in the toasted almonds.
Place 1/3-cup ovals of meringue on prepared baking sheets, about 6 per sheet. Bake 1 hour. Turn off heat; dry meringues in oven overnight. Store between layers of parchment in an airtight container in a cool, dry place up to 3 days.
Makes about 1 dozen meringues, best if allowed to dry overnight before serving