Cook blueberries with sugar and lemon juice, thicken with cornstarch, then cool completely.
Preheat oven to 325°F (160°C); mix cookie crumbs, butter, and sugar, press into a 9-inch pan, and bake 10 minutes.
Beat cream cheese with sugar, add eggs, sour cream, vanilla, cornstarch, and folded melted white chocolate.
Pour most batter over crust, add blueberry sauce, gently swirl, then pour remaining batter and swirl again.
Bake in a water bath 55–65 minutes; leave in oven with door cracked 1 hour.
Cool at room temperature, then refrigerate at least 4 hours or overnight.
Serve with extra blueberry sauce, fresh berries, white chocolate curls, or whipped cream.