Preheat your oven to 325°F (165°C). Grease a 9-inch springform pan.
In a medium bowl, mix graham cracker crumbs, 1/4 cup sugar, and melted butter. Press firmly into the bottom of the prepared pan.
In a saucepan over low heat, melt white chocolate chips with half-and-half, stirring until smooth. Set aside to cool slightly.
In a large bowl, beat cream cheese and 1/2 cup sugar until fluffy. Blend in eggs, one at a time. Stir in vanilla and melted white chocolate mixture until just combined.
Pour half the batter over the crust. In a small saucepan, combine blueberries, 2 tablespoons sugar, cornstarch, and water. Cook over medium heat until thickened, then cool slightly.
Spoon blueberry sauce over the batter in the pan. Top with remaining cheesecake batter and gently swirl with a knife.
Bake for 55 to 60 minutes, or until the center is almost set. Turn off oven, leave cheesecake inside for 1 hour.
Refrigerate at least 8 hours or overnight before removing from pan and serving.