We report on a novel microfluidic strategy for the continuous fabrication of monodisperse asymmetric vesicles with customized membrane composition, size, and luminal content. The microfluidic device encompasses a triangular post region and two flow-focusing regions. The major steps involved in the vesicle fabrication process include: (1) forming highly uniform water emulsions in an oil/inner-leaflet-lipid solution, (2) replacing the inner-leaflet-lipid solution with an outer-leaflet-lipid solution inside the microchannel network, (3) forming water-in-oil-in-water double emulsions, and (4) extracting excess oil/outer-leaflet-lipid solution from the double emulsions. Bilayer membrane asymmetry and unilamellarity are evaluated using a fluorescence quenching assay and a transmembrane protein insertion assay, respectively. Our approach addresses many of the deficiencies found in existing technologies for building vesicles, and yields strong membrane asymmetry. The ability to create and sustain membrane asymmetry is an important feature, as it is a characteristic of nearly all natural membranes. Over 80% of the vesicles remain stable for at least 6 weeks and the membrane asymmetry is maintained for over 30 hours. The asymmetric vesicles built using this strategy are collected off-chip and hold the potential to be used as model systems in membrane biology or as vehicles for drug delivery.