Preheat oven to 350° F.
Core apples, but do not peel.
Split apples in half and lay them, cut-side up, in a baking dish that will hold them upright.
Sprinkle with cinnamon, and bake on middle shelf of oven for about 30 minutes, or until tender when pierced with a knife point.
While apples are baking, beat egg whites in a small bowl until foamy throughout.
Sprinkle with cream of tartar, and continue beating until they form stiff peaks but are not dry.
Beat in vanilla.
Cover bowl with a plate.
When apples are tender, remove from oven and increase heat to 400 °F.
Divide meringue among apples, spooning an attractive mound on top of each.
Return to oven, and bake until meringue is golden brown.