Preheat the oven to 350 degrees F. Lightly grease an 8-inch square baking dish with cooking spray or butter.
Place the bread, in overlapping layers, in the prepared dish in 2 even rows.
In a large bowl, whisk together the dairy-free milk, sugar, vanilla and eggs. Pour evenly over the bread, pressing on the slices to help soak up the liquid.
Place the baking dish in a larger pan and pour in enough warm water to reach halfway up the sides of the dish. Bake until golden brown and the custard is set, about 50 minutes. Sift over confectioners' sugar, if using. Cut into 9 pieces and serve with berries.