The Dirac ensemble is a particular class of models for quantum gravity on finite noncommutative spaces in which one considers a family of random geometries ("metrics"), encoded by Dirac operators, over an underlying spectral triple. We investigate the large $N$ expansion of the correlation functions of a Dirac ensemble of type $(1,0)$ using the theory of blobbed topological recursion. Our model is based on a distribution of the form ${e^{- \mathcal{S} (D)} {\, \mathrm{d}} D}$ over the moduli space of Dirac operators in which the action functional ${\mathcal{S} (D)}$ is considered to be a sum of terms of the form ${\prod_{i=1}^s \mathrm{Tr} \left( {D^{n_i}} \right)}$. It leads to a multi-trace formal 1-Hermitian matrix model, where we use the blobbed topological recursion formula to obtain recursively-defined generating functions for enumerating the associated higher-genus maps. This talk is based on joint work with Masoud Khalkhali, arXiv:1906.09362.