We study a model in 1 + 2 dimensions composed of a spherical Fermi surface of N-f flavors of fermions coupled to a massless scalar. We present a framework to non-perturbatively calculate general fermion n-point functions of this theory in the limit N-f -> 0 followed by k(F) -> infinity where k(F) sets both the size and curvature of the Fermi surface. Using this frame-work we calculate the zero-temperature fermion density-density correlation function in real space and find an exponential decay of Friedel oscillations.