A building module. The building module has a rigid inner construction panel defining a planar surface thereon; one or more rigid brackets each affixed by one or more mechanical fasteners to the planar surface of the inner construction panel; a rigid, closed-cell, spray foam or adhesive matrix contiguous to and substantially covering the planar surface of the construction panel and filling and surrounding and/or embedding at least a major portion of the one or more brackets. Each of the one or more brackets bears a planar surface facing substantially away from the planar surface of the inner construction panel. The surface area of the planar surface of each of the one or more brackets is substantially smaller than the surface area of the planar surface of the construction panel to which it is affixed. There is also a method for making a building module, a method for constructing a building using the building module, and brackets useful in the building module.