In this letter, we present an approach for achieving precision post-stall landings with medium-sized Group 1 Unmanned Aerial Systems (UAS). To do this, we employ an aggressive dive-and-stall maneuver to significantly reduce maneuver distance, time, and touchdown speed. Our approach relies on a nonlinear model predictive control (NMPC) algorithm and learned aerodynamic coefficients to achieve accuracy and reliability in the presence of wind disturbances. We demonstrate our approach in hardware with a 60-inch wingspan, 4.2 kg fixed-wing UAS, and show the ability to land with low speed and high accuracy using minimal throttle.