  We stack the rest-frame ultraviolet spectra of N=14 highly magnified
gravitationally lensed galaxies at redshifts 1.6<z<3.6. The resulting new
composite spans $900< \lambda_{rest} < 3000$ \AA, with a peak signal-to-noise
ratio of 103 per spectral resolution element ($\sim$100 km/s). It is the
highest signal-to-noise ratio, highest spectral resolution composite spectrum
of $z\sim2$--3 galaxies yet published. The composite reveals numerous weak
nebular emission lines and stellar photospheric absorption lines that can serve
as new physical diagnostics, particularly at high redshift with the James Webb
Space Telescope (JWST). We report equivalent widths to aid in proposing for and
interpreting JWST spectra. We examine the velocity profiles of strong
absorption features in the composite, and in a matched composite of $z\sim0$
COS/HST galaxy spectra. We find remarkable similarity in the velocity profiles
at $z\sim 0$ and $z\sim2$, suggesting that similar physical processes control
the outflows across cosmic time. While the maximum outflow velocity depends
strongly on ionization potential, the absorption-weighted mean velocity does
not. As such, the bulk of the high-ionization absorption traces the
low-ionization gas, with an additional blueshifted absorption tail extending to
at least $-2000$ km/s . We interpret this tail as arising from the stellar wind
and photospheres of massive stars. Starburst99 models are able to replicate
this high-velocity absorption tail. However, these theoretical models poorly
reproduce several of the photospheric absorption features, indicating that
improvements are needed to match observational constraints on the massive
stellar content of star-forming galaxies at $z \sim 2$. We publicly release our
composite spectra.
