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Where the cosmic baryons lie in and around galactic dark matter halos is only weakly constrained. We develop a method to quickly paint on models for their distribution. Our approach uses the statistical advantages of $N$-body simulations, while painting on the profile of gas around individual halos in ways that can be motivated by semi-analytic models or zoom-in hydrodynamic simulations of galaxies. Possible applications of the algorithm include extragalactic dispersion measures to fast radio bursts (FRBs), the Sunyaev-Zeldovich effect, baryonic effects on weak lensing, and cosmic metal enrichment. As an initial application, we use this tool to investigate how the baryonic profile of foreground galactic-mass halos affects the statistics of the dispersion measure (DM) towards cosmological FRBs. We show that the distribution of DM is sensitive to the distribution of baryons in galactic halos, with viable gas profile models having significantly different probability distributions for DM to a given redshift. We also investigate the requirements to statistically measure the circumgalactic electron profile for FRB analyses that stack DM with impact parameter to foreground galaxies, quantifying the size of the contaminating "two-halo" term from correlated systems and the number of FRBs for a high significance detection. Publicly available Python modules implement our CGMBrush algorithm.