Soil moisture is a critical variable for managing irrigation, improving crop yield, and understanding field-scale hydrology. Radars mounted on unmanned aerial vehicles (UAVs) offer a promising means to monitor soil moisture over large fields with flexible, high-resolution coverage. However, during the growing season, canopy scattering and soil reflections become strongly coupled in the radar measurement. These coupled effects vary with crop structure or flight altitude, complicating the retrieval of soil moisture. To overcome this challenge, we present GreenScatter, a physics-based soil moisture retrieval framework for nadir-looking wideband UAV radars. GreenScatter introduces a microwave radiative transfer model that explicitly captures the dominant electromagnetic interactions between vegetation and soil, enabling accurate modeling of coherent ground backscatter through canopy. In parallel, it develops a radar cross-section (RCS) estimation method that transforms time-domain radar signals into calibrated wideband RCS spectra, isolating soil reflections while compensating for hardware and waveform effects. Together, these components enable robust soil moisture estimation through vegetation across varying canopy conditions and UAV configurations. Field experiments across multiple corn and soybean sites demonstrate consistent retrieval with an average volumetric water content (VWC) error of 4.49%.