Detached eclipsing binaries are a fundamental tool for measuring the physical parameters of stars that are effectively evolving in isolation. Starting from more than 40,000 eclipsing binary candidates identified by the All-Sky Automated Survey for Supernovae (ASAS-SN), we use PHOEBE to determine the sum of the fractional radii, the ratio of effective temperatures, the inclinations, and the eccentricities for 35,576 systems. We visually inspect all the light curve models to verify the model fits and examine the TESS light curves, when available, to select systems with evidence for additional physics, such as spots, mass transfer, and hierarchical triples. We examine the distributions of the eclipsing binary model parameters and the orbital parameters. We identify two groups in the sum of the fractional radii and effective temperature ratio parameter space that may distinguish systems approaching the semidetached limit. Combining Gaia EDR3 with extinction estimates from 3-dimensional dust maps, we examine the properties of the systems as a function of their absolute magnitude and evolutionary state. Finally, we present light curves of selected eclipsing binaries that may be of interest for follow-up studies.