Observations by HAWC and Milagro have detected bright and spatially extended TeV gamma-ray sources surrounding the Geminga and Monogem pulsars. We argue that these observations, along with a substantial population of other extended TeV sources coincident with pulsar wind nebulae, constitute a new morphological class of spatially extended TeV halos. We show that HAWCs wide field-of-view unlocks an expansive parameter space of TeV halos not observable by atmospheric Cherenkov telescopes. Under the assumption that Geminga and Monogem are typical middle-aged pulsars, we show that ten-year HAWC observations should eventually observe 37$^{+17}_{-13}$ middle-aged TeV halos that correspond to pulsars whose radio emission is not beamed towards Earth. Depending on the extrapolation of the TeV halo efficiency to young pulsars, HAWC could detect more than 100 TeV halos from mis-aligned pulsars. These pulsars have historically been difficult to detect with existing multiwavelength observations. TeV halos will constitute a significant fraction of all HAWC sources, allowing follow-up observations to efficiently find pulsar wind nebulae and thermal pulsar emission. The observation and subsequent multi-wavelength follow-up of TeV halos will have significant implications for our understanding of pulsar beam geometries, the evolution of PWN, the diffusion of cosmic-rays near energetic pulsars, and the contribution of pulsars to the cosmic-ray positron excess.
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