Mix cream cheese, confectioners' sugar, 2 tablespoons milk, and 1 teaspoon vanilla extract in a bowl until smooth and creamy; fold in 1 cup blueberries.
Cover the bottom of a 10x14-inch baking dish with a layer of bread cubes. Spread cream cheese mixture over bread layer; top with remaining bread cubes.
Whisk 2 cups milk, eggs, 2 teaspoons vanilla extract, cinnamon, and nutmeg together in a large bowl; pour over bread mixture. Sprinkle 1 cup blueberries over bread-egg mixture. Cover dish tightly with aluminum foil and refrigerate, 8 hours to overnight. Remove from refrigerator 30 to 60 minutes before baking.
Preheat the oven to 375 degrees F (190 degrees C).
Bake in the preheated oven for 45 minutes. Remove foil and continue baking until the center is set, about 30 minutes.