High-resolution X-ray imaging of noncrystalline objects is often achieved through the approach of scanning coherent diffractive imaging known as ptychography. The imaging resolution is usually limited by the scattering properties of the sample, where weak diffraction signals at the highest scattering angles compete with parasitic scattering. Here, we demonstrate that X-ray multilayer Laue lenses with a high numerical aperture (NA) can be used to create a strong reference beam that holographically boosts weak scattering from the sample over a large range of scattering angles, enabling high-resolution imaging that is tolerant of such background. An imaging resolution of sub-10 nm was achieved at a photon energy of 17.4 keV with lenses of 0.014 NA from a Siemens star test object and a sample of hierarchical nanoporous gold, recording projection holograms at an effective magnification of more than 30,000 directly on a pixel-array detector. A numerical study compared this approach to low-NA far-field ptychography, indicating significant advantages for using high-NA lenses in the presence of background noise. This imaging modality is particularly fast and efficient at recording high-resolution transmission phase-contrast images over large fields of view in a facile manner.