Lightly grease a 9x9-inch square baking dish or 2.5-quart casserole dish.
CUT BREAD INTO CHUNKS: Preheat oven to 300F. Using your favorite grain-free bread, cut into slices and then even-sized chunks or cubes. Spread out onto a baking sheet. Bake for 10 minutes and then flip and bake for another 10 minutes. Once cooled add them to the bottom of greased casserole dish.
Make the streusel topping: In a medium bowl, combine the flour, brown sugar, cinnamon and salt together. Cut in the cubed butter with a pastry blender or two forks.
Arrange half of the bread cubes in the bottom of the pan. Pour with 1/3 of the egg mixture and sprinkle with 1/3 of the streusel topping. Top with remaining bread cubes. Pour in remaining egg mixture, pressing down the bread cubes to absorb mixture.
Meanwhile, make the icing: Combine maple syrup, cream cheese and milk in a medium bowl and whisk until smooth. Add more or less milk depending on consistency desired.