Fill a cocktail shaker or small pitcher with ice. Add the apple jack, lemon juice, and grenadine. Cover and shake vigorously until thoroughly mixed and chilled, about 30 seconds. (In general, the drink is ready by the time the shaker mists up.) Strain into 2 Champagne flutes. Top each drink off with 1 1/2 ounces Champagne. Garnish with the apple. Drink.
Put pomegranate juice in a small sauce pan. Bring to a boil over high heat. Reduce the heat to a gentle simmer and continue to cook until liquid is reduced by half. Stir in the sugar to dissolve thoroughly, and simmer to thicken slightly. Cool. Cover and refrigerate for up to 2 weeks.
From Food Network Kitchens