Heat heavy cream in a small pot over medium high heat until almost boiling. In a separate bowl whisk together 6 egg yolks with 4 tbsp sugar until combined. Slowly pour about 1/4 cup of the hot cream into the egg yolk mixture and whisk briskly. Then slowly pour the egg/cream mixture into the hot cream and keep whisking till combined.
Skim off the foam from the cream mixture and discard. Add vanilla, cream cheese, and sour cream and whisk until smooth and combined. Skim off any excess foam and discard.
Arrange ramekins in a baking dish. Evenly divide the Crème Brûlée mixture into the ramekins and top with fresh blueberries. Fill the baking dish with hot water until it comes half way up the sides of the ramekins, being careful not to get any water into the ramekins.
Bake 15-30 minutes until set, but center is still slightly jiggly. Carefully remove from oven and let cool on wire rack for 20 minutes, then chill in fridge for 2 hours (or up to 3 days).
Combine the remaining white sugar with the brown sugar and sprinkle evenly on top of Crème Brûlée. Use a kitchen torch to caramelize the sugar so it becomes crisp. Or you can place the ramekins in a baking dish filled with ice water and place it under the broiler for a few minutes till the sugar gets crisp.