With an electric mixer, beat egg white and cream of tartar until very foamy. Gradually sprinkle in sugar, about 1 tbsp. at a time, beating well after each addition. Beat until meringue holds very stiff, shiny peaks, at least 10 minutes. Add vanilla; beat about 30 seconds longer.
Preheat oven to 225°. Cover a baking sheet with parchment. On it, draw 4 heart shapes, each 3 in. at the widest point. Turn parchment over and, with a knife, spread meringue 1/4 in. thick over each heart shape, building up sides so they stand an additional 1/2 to 3/4 in. high.
Bake meringues for 45 minutes. Turn off oven and let meringues dry in oven for 1 1/2 hours. If making ahead, see Notes.
About 1 to 2 hours before serving, fill each meringue with softened frozen yogurt. Place in freezer and chill until firm, at least 1 hour. Top hearts with white chocolate curls and serve.
Note: Nutrition analysis is per meringue.