Hollow-core optical fibers can offer broadband, single mode guidance in the UV-visible-NIR wavelength range, with the potential for low-loss, solarization-free operation, making them desirable and potentially disruptive for a wide range of applications. To achieve this requires the fabrication of fibers with <300nm anti-resonant membranes, which is technically challenging. Here we investigate the underlying fluid dynamics of the fiber fabrication process and demonstrate a new three-stage fabrication approach, capable of delivering long (∼350m) lengths of fiber with the desired thin-membranes.