We report the continuous production of microcapsules composed of an aqueous core and permeable hydrogel shell, made stable by the controlled photo-cross-linking of the shell of an all-aqueous double emulsion. While most previous work on water-based emulsions focused on active droplet formation, here double emulsion droplets were spontaneously generated at a three-dimensional flow-focusing junction through the break-up of a double jet formed by immiscible aqueous solutions of polyethylene glycol and cross-linkable dextrans. The capsules obtained with this lipid-free, organic-solvent-free, and surfactant-free approach displayed excellent stability under a variety of harsh conditions (3 <pH <13, high salinity). Drying and rehydration experiments demonstrate the permeability of the shell, which may enable molecular-weight-dependent release and uptake of polar solutes.