How to Make It
Preheat oven to 250°F. Beat together egg whites, vanilla, and cream of tartar with an electric stand mixer with the whisk attachment on high speed until foamy, about 1 minute. Slowly sprinkle in 1/4 cup of the sugar, and continue to beat until stiff peaks form, about 1 more minute. Spread meringue in a 1/2-inch layer over a silicone mat or a large rimmed baking sheet lined with parchment paper. Bake in preheated oven until lightly browned and firm, 60 to 70 minutes. Let cool completely, about 2 hours, at room temperature. Break into bite-sized pieces.
While meringue cools, toss together strawberries, basil leaves, and 1 tablespoon of the sugar in a bowl. Let stand, tossing occasionally, until strawberries have released liquid and have become syrupy, about 1 hour.
When ready to serve, beat together cream and remaining 1 tablespoon sugar in a cold medium bowl with electric mixer on medium-high speed until medium peaks form, about 2 minutes. Gently fold in yogurt. Divide broken meringue pieces among 8 (8-oz.) cups; layer with whipped yogurt, and top with berries. Repeat layers, ending with a sprinkle of meringue on top. Garnish with basil. Serve within 20 minutes of preparing.