Cloud microphysical parameterizations in atmospheric models describe the formation and evolution of clouds and precipitation, a central weather and climate process. Cloud-associated latent heating is a primary driver of large and small-scale circulations throughout the global atmosphere, and clouds have important interactions with atmospheric radiation. Clouds are ubiquitous, diverse, and can change rapidly. In this work, we build the first emulator of an entire cloud microphysical parameterization, including fast phase changes. The emulator performs well in offline and online (i.e. when coupled to the rest of the atmospheric model) tests, but shows some developing biases in Antarctica. Sensitivity tests demonstrate that these successes require careful modeling of the mixed discrete-continuous output as well as the input-output structure of the underlying code and physical process.