In a 9-inch cheesecake pan with removable rim (at least 1 3/4 in. tall), mix graham cracker crumbs and butter. Pat mixture evenly over bottom and about 1/2 inch up sides of pan.
Bake crust in a 350° regular or convection oven until slightly browner, 8 to 10 minutes.
In a 1- to 1 1/2-quart pan, mix gelatin with 2 tablespoons cold water; let stand until softened, about 1 minute. Stir over medium heat until gelatin is dissolved, about 45 seconds. Remove from heat and stir in liqueur and vanilla.
In a large bowl, with a mixer on medium speed, beat cheese, sugar, and gelatin mixture until smooth. Beat in eggs, one at a time, until smoothly blended. Pour mixture into hot or cool crust.
Bake cheesecake in a 325° regular or 300° convection oven until center jiggles only slightly when pan is gently shaken, 30 to 35 minutes. Cool cake on a rack for about 30 minutes, then chill, uncovered, until cold, at least 2 hours. Serve, or cover airtight and chill up to 1 day.
Just before serving, lightly blot any moisture from surface of cake with a paper towel. Spread cranberry sauce evenly over cake. Remove pan rim and cut cake into wedges.
Nutritional analysis per serving with yogurt cheese: 259 cal., 15% (39 cal.) from fat; 9 g protein; 3 g fat (8 g sat.); 48 g carbo (1 g fiber); 116 mg sodium; 77 mg chol.
Nutritional analysis per serving with cream cheese: 419 cal., 52% (216 cal.) from fat; 9 g protein; 24 g fat (14 g sat.); 45 g carbo (1 g fiber); 251 mg sodium; 138 mg chol.