Grease a 9x13 inch baking dish with butter. Cut 10 slices of the bread into 3/4 inch cubes. Spread Neufchatel cheese over one side of the remaining 6 slices of bread. Arrange the bread, cheese side up, in the baking dish. Sprinkle with 1 cup of the blueberries, then top with the bread cubes.
Whisk together the milk, eggs, maple syrup, vanilla extract, and 1/4 cup of sugar in a bowl. Pour over the bread. Cover and refrigerate overnight.
Preheat an oven to 350 degrees F (175 degrees C).
Mix together the nutmeg and 1/4 cup of sugar in a small bowl. Sprinkle over bread mixture. Cover with foil and bake in the preheated oven until a knife inserted into the center comes out clean, 20 to 30 minutes. Cool in the pan for 5 minutes before serving.
To make compote: Heat cornstarch, water and remaining 1 cup of sugar over medium heat and bring to a simmer, cooking until thickened, about 3 minutes. Remove from heat and stir in butter and the remaining 1 cup of blueberries. Serve with the french toast.
