Preheat your oven to 350°F (175°C). Grease a 9x13-inch baking dish with butter or non-stick cooking spray.
Tear the croissants into 1 to 2-inch chunks and spread them evenly in the prepared baking dish. Scatter the blueberries and raspberries over the croissant pieces.
In a large mixing bowl, whisk together the eggs, whole milk, heavy cream, granulated sugar, brown sugar, vanilla extract, cinnamon, and salt until the mixture is completely smooth and the sugars are dissolved.
Cut the softened cream cheese into small cubes and distribute them evenly over the croissant and berry mixture. Slowly and evenly pour the egg mixture over the entire casserole, ensuring all the croissant pieces are moistened. Gently press down on the top with a spatula to help the bread soak up the custard.
Let the casserole stand for 15 minutes to allow the bread to fully absorb the liquid. Bake for 45 to 55 minutes, or until the top is puffed and golden brown and the center is set (a knife inserted near the center should come out clean).
Remove the casserole from the oven and let it rest for 10 minutes before serving. Dust the top generously with powdered sugar just before slicing.