The efficiency of perovskite solar cells (PSCs) is currently limited by non-radiative recombination losses. One potential loss channel consists of electrons recombining at the interface with the hole transport layer (HTL). We synthesized adamantylammonium halides (ADAHX, X = Cl-, Br-, I-) and demonstrated that ADAHI interacts with the perovskite surface using solid-state NMR spectroscopy. As a result, ADAHI reduces non-radiative recombination when added to the HTL, raising the PSC photovoltage to an average value of 1.185 V, the power conversion efficiency (PCE) to almost 22%, and the maximum external electroluminescence quantum yield to 2.5% at an injection current that is equal to the photocurrent under solar illumination. The lowest value measured for the loss in potential is only 365 mV with respect to the band gap, surpassing the highest-efficiency silicon solar cells. Devices with ADAHI-modified HTL show excellent operational stability for 500 hours. We show the general validity of our new approach for a variety of perovskite formulations and hole conductors.