To prepare yogurt cheese, place a colander in a medium bowl. Line colander with 2 layers of cheesecloth, allowing cheesecloth to extend over outside edge. Spoon yogurt into the colander. Cover loosely with plastic wrap; refrigerate 12 hours. Spoon yogurt cheese into a bowl; discard liquid. Cover and refrigerate.
Preheat oven to 350°.
To prepare crust, combine cracker crumbs and butter, tossing with a fork until moist. Press into bottom of a 9-inch springform pan coated with cooking spray. Bake at 350° for 10 minutes; cool on a wire rack. Reduce oven temperature to 300°.
To prepare cranberry jam, combine the cranberries, 1/2 cup sugar, water, and juice in a medium, heavy saucepan. Bring to a boil over medium-high heat. Cover, reduce heat to medium-low, and simmer 10 minutes or until cranberries are soft. Remove from heat, and cool slightly. Place cranberry mixture in a food processor; process 2 minutes or until almost smooth. Set aside.
To prepare filling, place chocolate and milk in the top of a double boiler. Cook over simmering water 5 minutes or until chocolate melts and mixture is smooth, stirring constantly. Remove from heat; stir in vanilla. Set aside.
Place yogurt cheese, 1 cup sugar, and next 4 ingredients (1 cup sugar through sour cream) in a large bowl, and beat with a mixer at low speed 1 minute. Beat at medium-high speed 2 minutes or until smooth, scraping bowl occasionally. Beat in chocolate mixture. Add eggs, 1 at a time, beating well after each addition. Scrape bowl, and beat 30 seconds. Fold in cranberry jam. Pour over crust, and smooth top. Loosely cover with aluminum foil.
Bake at 300° for 1 hour and 10 minutes. Turn oven off; remove foil. Cool cheesecake in closed oven 1 hour and 15 minutes. Remove cheesecake from oven; run a knife around outside edge. Cool to room temperature. Cover and chill at least 8 hours.