Preheat the oven to 300 degrees F (150 degrees C). Butter and sugar a 2-quart baking dish.

Combine prunes and 1/3 cup water in a medium saucepan over medium heat; bring to a simmer and cook until soft, about 5 minutes. Drain.

Purée prunes in a blender, then transfer back to the saucepan. Add 1/3 cup sugar and heat until sugar dissolves. Remove from the heat and stir in lemon juice and vanilla.

Beat egg whites in a glass, metal, or ceramic bowl until frothy. Add cream of tartar and continue to beat until stiff peaks form. Fold in prune purée. Pour mixture into the prepared baking dish.

Bake in the preheated oven until nicely browned on top, 15 to 20 minutes. Cool to room temperature, then chill for at least 2 hours before serving.