Over the past 15 years, examples of exotic radio-quiet quasars with intrinsically weak or absent broad emission line regions (BELRs) have emerged from large-scale spectroscopic sky surveys. Here, we present spectroscopy of seven such weak emission line quasars (WLQs) at moderate redshifts (z = 1.4 − 1.7) using the X-shooter spectrograph, which provides simultaneous optical and nearinfrared spectroscopy covering the rest-frame ultraviolet through optical. These new observations effectively double the number of WLQs with spectroscopy in the optical rest-frame, and they allow us to compare the strengths of (weak) high-ionization emission lines (e.g., C IV) to low-ionization lines (e.g., Mg II, Hβ, Hα) in individual objects. We detect broad Hβ and Hα emission in all objects, and these lines are generally toward the weaker end of the distribution expected for typical quasars (e.g., Hβ has rest-frame equivalent widths ranging from 15-40Å.). However, these low-ionization lines are not exceptionally weak, as is the case for high-ionization lines in WLQs. The X-shooter spectra also display relatively strong optical Fe II emission, Hβ FWHM 4000 km s −1 , and significant C IV blueshifts (≈1000-5500 km s −1 ) relative to the systemic redshift; two spectra also show elevated ultraviolet Fe II emission, and an outflowing component to their (weak) Mg II emission lines. These properties suggest that WLQs are exotic versions of "wind-dominated" quasars. Their BELRs either have unusual high-ionization components, or their BELRs are in an atypical photoionization state because of an unusually soft continuum.