uDALES is an open-source multi-physics microscale urban modelling framework, capable of performing large-eddy simulation (LES) of urban airflow, heat transfer, and pollutant dispersion. We present uDALES v2.0, which has two main new features: 1) an improved parallelisation that prepares the codebase for conducting exascale simulations; and 2) a conservative immersed boundary method (IBM) suitable for an urban surface that does not need to be aligned with the underlying Cartesian grid. The urban geometry and local topography are incorporated via a triangulated surface with a resolution that is independent of the fluid grid. The IBM developed here includes the use of wall functions to apply surface fluxes, and the exchange of heat and moisture between the surface and the air is conservative by construction. We perform a number of validation simulations, ranging from neutral, coupled internal-external flows and non-neutral cases. Good agreement is observed, both in cases in which the buildings are aligned with the Cartesian grid and when they are at an angle. We introduce a validation case specifically for urban applications, for which we show that supporting non grid-aligned geometries is crucial when solving surface energy balances, with errors of up to 20 % associated with using a previous version of uDALES.