Preheat oven to 375 degrees F. Grease four 6-ounce custard cups or souffle dishes and sprinkle with 1 tablespoon sugar.
Using a large bowl, with a wire whisk, mix apricot jam with vanilla.
In another large bowl, with mixer on high speed, beat egg whites and cream of tartar until soft peaks form. Beating at high speed, gradually sprinkle in remaining 1 tablespoon sugar until mixture holds stiff peaks when beaters are lifted.
With rubber spatula, gently fold one-third of beaten whites into apricot mixture. Fold in remaining whites, half at a time. Spoon mixture into custard cups. (Mixture will fill cups completely.)
With metal spatula held at a 45-degree angle to souffle, make a doomed peak on each souffle. Place cups on jelly-roll pan for easier handling. Bake souffles until puffed and golden, 12 to 15 minutes. Serve immediately.