Energy storage structures and fabrication methods are provided. The method include: providing first and second conductive sheet portions separated by a permeable separator sheet, and defining, at least in part, outer walls of the energy storage structure, the first and second surface regions of the first and second conductive sheet portions including first and second electrodes facing first and second (opposite) surfaces of the permeable separator sheet; forming an electrolyte receiving chamber, defined, at least in part, by the first and second surface regions, including: bonding the first and second conductive sheet portions, and the permeable separator sheet together with at least one bonding border forming a bordering frame around at least a portion of the first and second electrodes; and providing an electrolyte within the electrolyte receiving chamber, including in contact with the first and second electrodes, with the electrolyte being capable of passing through the permeable separator sheet.