Line an 8 x 8 baking pan with foil. Set aside.
In a small saucepan combine the blueberries, lemon juice, sugar and cornstarch. Heat over medium low heat, stirring frequently, until the blueberries start to burst.
Crush the blueberries as best you can and increase the heat to medium. Cook for 5-10 minutes, stirring frequently so it doesn't burn, cook until the mixture is thick. Remove from heat.
In a medium saucepan combine the sweetened condensed milk and white chocolate. Cook over medium low heat, stirring frequently, until the chocolate has melted and the mixture is smooth.
Add in the butter and cook, stirring frequently, until the butter has melted. Stir in the vanilla. Remove from heat.
Remove 3 tablespoons of the blueberry mixture from the pan. Pour the blueberries left in the pan on top of the white chocolate mixture. Using a rubber spatula turn the mixture 3 times just to get it swirled but not mixed together. Pour into prepared pan.
Place dollops of the remaining blueberries on top of the fudge and use a butter knife to swirl it into the fudge.
Refrigerate for at least 3 hours.
Remove from refrigerator and use foil to pull it out of the pan. Cut into squares and serve.