Notes: For the Yogurt Cheese, drain 2 1/2 to 3 quarts nonfat yogurt at least 24 hours. If using cream cheese, omit the gelatin and step 3; in step 4, beat in the liqueur and vanilla until smooth, then beat in eggs. Hachiya persimmons need to be as soft as jelly for this glaze. If they're too firm, let them stand at room temperature for a few days until fully ripe.
1 cup graham cracker crumbs
2 tablespoons butter or margarine, melted
1 1/2 teaspoons unflavored gelatin
2 tablespoons orange-flavor liqueur or orange juice
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. If making up to 1 day ahead, cover cold cake airtight and chill.
Just before serving, lightly blot any moisture from surface of cake with a paper towel. Spread Persimmon Glaze over the cool or cold cake. Chill until firm, at least 15 minutes. To chill longer, cover cheesecake when glaze is set.
Persimmon Glaze: Rinse 2 or 3 soft-ripe Hachiya persimmons (each 2 1/2 to 3 in. wide, about 1 1/2 lb. total; see notes). Cut them in half and scoop out the soft flesh; discard stems and peels. In a blender or food processor, whirl flesh until puréed (you need 1 1/2 cups; save any extra for other uses). In a 1- to 2-quart pan, mix 1 tablespoon sugar with 1 1/2 teaspoons cornstarch. Add the 1 1/2 cups persimmon purée and stir over medium heat until mixture boils and thickens, about 4 minutes. Nest pan in a bowl of ice water and stir mixture until it's cool but still fluid, about 3 minutes. Immediately spread evenly over cool or cold cheesecake.