Preheat oven to 350°F and grease a baking dish.
In a bowl, combine blueberries, sugar, cornstarch, and lemon juice. Pour into the prepared baking dish.
In another bowl, beat cream cheese, sugar, egg, and vanilla until smooth. Drop spoonfuls over the blueberry mixture.
In a separate bowl, whisk together flour, sugar, baking powder, and salt. Stir in milk and melted butter until just combined.
Spoon cobbler batter evenly over the blueberry and cream cheese layers.
Bake for 40–45 minutes until golden brown and bubbly.
Allow to cool slightly before serving warm.