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We present a robust sample of very high-redshift galaxy candidates from thefirst epoch of {\it JWST}/NIRCam imaging from the Next Generation ExtragalacticExploratory Deep (NGDEEP) Survey. The NGDEEP NIRCam imaging in the Hubble UltraDeep Field Parallel Field 2 (HUDF-Par2) reaches $m=30.4$ (5$\sigma$,point-source) in F277W, making it the deepest public {\it JWST} GO imagingdataset to date. We describe our detailed data reduction process of thesix-filter broad-band {\it JWST}/NIRCam imaging, incorporating customcorrections for systematic effects to produce high-quality calibrated images.Using robust photometric redshift selection criteria, we identify a sample of38 $z \gtrsim 9$ galaxy candidates. These objects span a redshift range of$z=8.5-15.8$, and apparent magnitudes of $m_\mathrm{F277W} = 27-30.5$ AB mag,reaching $\sim 1.5$ mag deeper than previous public {\it JWST} imaging surveys.We calculate the rest-frame ultraviolet (UV) luminosity function at $z \sim$ 9and 11, and present a new measurement of the luminosity function faint-endslope at $z \sim 11$. There is no significant evolution in the faint-end slopeand number density from $z=9$ to 11. Comparing our results with theoreticalpredictions, we find that some models produce better agreement at the faint endthan the bright end. These results will help to constrain how stellar feedbackimpacts star formation at these early epochs.

NGDEEP Epoch 1: The Faint-End of the Luminosity Function at $z \sim$ 9-12 from Ultra-Deep JWST Imaging