High-contrast adaptive optics (AO) observations near stars have to contend with the telescope's diffraction halo, a rapidly-changing cloud of residual atmospheric speckles, and a host of faint but persistent quasi-static speckles caused by various imperfections and aberrations. It is these quasi-static speckles that typically limit the detection sensitivity near stars as they are easily confused with faint stellar companions. Since they are coherent with the starlight, it is possible to suppress the quasi-static speckles and other residual diffraction halo over a search region by applying small offsets to the AO system's deformable mirror (DM). Computing the required offsets requires knowledge of the location, brightness, and phase of the speckle relative to the star's PSF core. We present a new wavefront sensing technique for measuring the static halo that uses the randomly-changing residual AO speckles as interferometric probes. Doing this requires simultaneous short-exposure frames from a mid-IR science camera and measurements of the residual closed-loop wavefront using the AO system's wavefront sensor (WFS). These data streams are combined to construct a map of the quasi-static halo's complex amplitude near the bright core of a star's PSF, permitting adaptive halo suppression. Implementing this new WFS and halo-suppression servo requires no new hardware, just new processing applied to the existing AO system. By suppressing the quasi-static speckles, we are left with only the fast speckle noise, which should average to a smooth background.