Computational models of cloud formation typically use homogeneous nucleation to predict the ice nucleated in supercooled water. However, the existence of ultra viscous organic aerosol in the upper troposphere has offered alternative ice nucleation pathways, which have been observed in laboratory studies. The possible effects of aerosol viscosity on cloud micro-physical properties have traditionally been interpreted from simple model simulations of an individual aerosol particle based on equilibration timescales. In this study, to gain insight into the formation of ice in an ensemble of ultra viscous aerosol particles, we have developed the first cloud parcel model with bin micro-physics to simulate condensed phase diffusion through each individual aerosol particle. Our findings demonstrate, for the first time, the complex relationship between the rate of ice formation and the viscosity of secondary organic aerosol, driven by two competing effects - which cannot be explained using existing modelling approaches. The first is inhibition of homogeneous ice nucleation below 200K, due to restricted particle growth and low water volume. The second occurs at temperatures between 200K and 220K, where water molecules are slightly more mobile and a layer of water condenses on the outside of the particle, causing an increase in the number of frozen aerosol particles. Our new model provides a basis to better understand and simulate ice cloud formation on a larger scale, addressing a major source of uncertainty in climate modelling through the representation of micro-physical cloud processes.