While small, Neptune-like planets are among the most abundant exoplanets, our understanding of their atmospheric structure and dynamics remains sparse. In particular, many unknowns remain on the way moist convection works in these atmospheres where condensable species are heavier than the non-condensable background gas. While it has been predicted that moist convection could shutdown above some threshold abundance of these condensable species, this prediction is based on simple linear analysis and relies on some strong assumptions on the saturation of the atmosphere. To investigate this issue, we develop a 3D cloud resolving model for hydrogen-dominated atmospheres with large amounts of condensable species and apply this model to a prototypical temperate Neptune-like planet-K2-18 b. Our model confirms the shutdown of moist convection above a critical abundance of condensable vapor and the onset of a stably stratified layer in the atmosphere of such planets, leading to much hotter deep atmospheres and interiors. Our 3D simulations further provide quantitative estimates of the turbulent mixing in this stable layer, which is a key driver of the cycling of condensables in the atmosphere. This allows us to build a very simple, yet realistic 1D model that captures the most salient features of the structure of Neptune-like atmospheres. Our qualitative findings on the behavior of moist convection in hydrogen atmospheres go beyond temperate planets and should also apply to the regions where iron and silicates condense in the deep interior of hydrogen-dominated planets. Finally, we use our model to investigate the likelihood of a liquid ocean beneath a H 2 dominated atmosphere on K2-18 b. We find that the planet would need to have a very high albedo (A > 0.5-0.6) to sustain a liquid ocean. However, due to the spectral type of the star, the amount of aerosol scattering that would be needed to provide such a high albedo is inconsistent with the latest observational data.