Preheat oven to 350 degrees F.
In a mixing bowl, place graham cracker crumbs and melted butter. Mix well and pat into the bottom and sides of a well-buttered 9-inch pie dish. Sent aside.
In a large mixing bowl, beat cream cheese, goat cheese, and sugar with an electric beater until creamy. Add eggs and beat on low speed until well incorporated. Stir in yogurt and vanilla.
Pour batter into the pie dish lined with the crust and bake for 30 minutes, or until the center is barely jiggly. (Time may vary from oven to oven.) Remove from the oven for about 10 minutes. Increase oven temp to 425 degrees F.
Meanwhile, mix 1/2 cup yogurt, 1/4 cup sugar, and 1 tablespoon vanilla in a small bowl. After the cheesecake has set out for the 10 minutes, carefully spread this mixture over the top and bake again for about 10 more minutes. Remove from the oven. Cool completely and then refrigerate until cold. Serve cheesecake cold with compote spooned over the top.