According to Lambda-CDM theory, star formation at high redshift should be primarily sustained by steady cold accretion from the Intergalactic Medium (IGM). However, there is little observational support for such inflows of pristine material. In this study we examine this issue by using QSO absorption line systems at z~2. In particular, we use high S/N UVES spectra of lensed QSOs with projected line-of-sight separations of ∼2 kpc. These separations are expected to uncover kinematic signatures of cold flows as seen in HI absorption at the level of ~x10 km/s. We use ~15 metal systems as signposts for galaxies close in projection (but otherwise not detected), for which we detect a total of ∼50 velocity components that are also seen in Ly-alpha and/or Ly-beta. As opposed to Ly-alpha forest lines, most of these components show kinematic differences but not all have associated metals, down to stringent limits. Our hypothesis is that the latter correspond to sightlines crossing pristine gas inflows from the IGM. We discuss the fraction of candidates in the context of the predicted covering fraction of cold-flows at Cosmic Noon.