We present a large spectroscopic survey with \textit{JWST}'s Mid-Infrared Instrument (MIRI) Low Resolution Spectrometer (LRS) targeting
37 infrared-bright galaxies between
z=0.65−2.46 with infrared luminosities
logLIR/L⊙>11.5 and
logM∗/M⊙=10−11.5. Targets were taken from a \textit{Spitzer}
24μm-selected sample with archival spectroscopy from the Infrared Spectrograph (IRS) and include a mix of star-forming galaxies and dust-obscured AGN. By combining IRS with the increased sensitivity of LRS, we expand the range of spectral features observed between
5−30μm for every galaxy in our sample. In this paper, we outline the sample selection, \textit{JWST} data reduction, 1D spectral extraction, and polycyclic aromatic hydrocarbon (PAH) feature measurements from
λrest=3.3−11.2μm. In the \textit{JWST} spectra, we detect PAH emission features at
3.3−5.3μm, as well as Paschen and Brackett lines. The
3.3μm feature can be as bright as
1% of the
8−1000μm infrared luminosity and exhibits a tight correlation with the dust-obscured star-formation rate. We detect absorption features from CO gas, CO
2 ice, H
2O ice, and aliphatic dust. From the joint \textit{JWST} and \textit{Spitzer} analysis we find that the
11.3/3.3μm PAH ratios are on-average three times higher than that of local luminous, infrared galaxies. This is interpreted as evidence that the PAH grains are larger at
z∼1−2. The size distribution may be affected by coagulation of grains due to high gas densities and low temperatures. These conditions are supported by the observation of strong water ice absorption at
3.05μm, and can lower stellar radiative feedback as large PAHs transmit less energy per photon into the interstellar medium.