Sea ice production within polynyas, an outcome of the atmosphere - ice - ocean interaction, is a major source of dense water and hence key to the global overturning circulation, but is poorly quantified over open-ocean polynyas. Using the two recent extensive open-ocean polynyas within the wider Maud Rise region of the Weddell Sea in 2016 and 2017, we here explore the surface ice energy budget and estimate their ice production based on satellite retrievals, in-situ hydrographic observations, and the Japanese 55-year Reanalysis (JRA55). We find that the oceanic heat flux amounts to 36.1 and 30.7 W m-2 within the 2016 and 2017 polynyas, respectively. We find that the 2017 open-ocean polynya produced nearly 200 km3 of new sea ice, which is comparable to the production in the largest Antarctic coastal polynyas. Finally, we find that ice production is highly correlated with the 2 m air temperature and wind speed, which affect the turbulent fluxes. It is also highly sensitive to uncertainties in the atmospheric air temperature and mixed layer depth, which urgently need to be better monitored at high latitudes.