We present the pilot study component of the Fluorescent Lyman-Alpha Structures in High-z Environments (FLASHES) Survey; the largest integral-field spectroscopy survey to date of the circumgalactic medium at $z=2.3-3.1$. We observed 48 quasar fields between 2015 and 2018 with the Palomar Cosmic Web Imager (Matuszewski et al. 2010). Extended HI Lyman-$mathrm{alpha}$ emission is discovered around 42/48 of the observed quasars, ranging in projected, flux-weighted radius from 21-71 proper kiloparsecs (pkpc), with 26 nebulae exceeding $100mathrm{~pkpc}$ in effective diameter. The circularly averaged surface brightness radial profile peaks at a maximum of $mathrm{1times 10^{-17}~erg~s^{-1}~cm^{-2}~arcsec^{-2}}$ ($2times10^{-15}~mathrm{erg~s^{-1}~cm^{-2}~arcsec^{-2}}$ adjusted for cosmological dimming) and luminosities range from $1.9times10^{43}~mathrm{erg~s^{-1}}$ to $-14.1times10^{43}~mathrm{erg~s^{-1}}$. The emission appears to have a highly eccentric morphology and a maximum covering factor of $50%$ ($60%$ for giant nebulae). On average, the nebular spectra are red-shifted with respect to both the systemic redshift and Ly$alpha$ peak of the quasar spectrum. The integrated spectra of the nebulae mostly have single or double-peaked line shapes with global dispersions ranging from $167~mathrm{km~s^{-1}}$ to $690~mathrm{km~s^{-1}}$, though the individual (Gaussian) components of lines with complex shapes mostly appear to have dispersions $leq 400$ $mathrm{km~s^{-1}}$, and the flux-weighted velocity centroids of the lines vary by thousands of $ mathrm{km~s^{-1}}$ with respect to the systemic QSO redshifts. Finally, the root-mean-square velocities of the nebulae are found to be consistent with gravitational motions expected in dark matter halos of mass $mathrm{M_h simeq10^{12.5} M_odot}$. We compare these results to existing surveys at both higher and lower redshift.
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