We compute for the spectrum for emitting 1 and 2 soft and collinear gluons from a hard scattering process in full QCD. This result is important because 1) all current energy loss calculations assume QED-like independent emissions of multiple gluons, which obviously misses all correlations from the non-Abelian nature of QCD, and 2) the average high-$p_T$ parton emits $\sim$3 gluons as it escapes the medium. QCD correlations are therefore critical for any realistic comparison of theoretical predictions to experimental data on jets and jet substructures in heavy ion collisions. These calculations additionally provide a benchmark for jet Monte Carlo algorithms.