Expansive cirrus clouds present above the anvils of extratropical convection have been observed in satellite and aircraft-based imagery for several decades. Despite knowledge of their occurrence, the precise mechanisms and atmospheric conditions leading to their formation and maintenance are not entirely known. Here, the formation of these cirrus "plumes" is examined using a combination of satellite imagery, four-dimensional ground-based radar observations, assimilated atmospheric states from a state-of-the-art reanalysis, and idealized numerical simulations with explicitly resolved convection. Using data from 20 recent events (2013-present), it is found that convective cores of storms with above-anvil cirrus plumes reach altitudes 1-6 km above the tropopause. Thus, it is likely that these clouds represent the injection of cloud material into the lower stratosphere. Comparison of storms with above-anvil cirrus plumes and observed tropopause-penetrating convection without plumes reveals an association with large vector differences between the motion of a storm and the environmental wind in the upper troposphere and lower stratosphere (UTLS), suggesting that gravity wave breaking and/or stretching of the tropopause-penetrating cloud are/is more prevalent in plume-producing storms. A weak relationship is found between plume occurrence and the stability of the lower stratosphere (or tropopause structure), and no relationship is found with the duration of stratospheric penetration or stratospheric humidity. Idealized model simulations of tropopause-penetrating convection with small and large magnitudes of storm-relative wind in the UTLS are found to reproduce the observationally established storm-relative wind relationship and show that frequent gravity wave breaking is the primary mechanism responsible for plume formation.