In this talk I will present the computation of the partition function of finite cut-off JT gravity (with positive, zero or negative curvature) defined on a disk and coupled to conformal matter with central charge c. The analysis is done in a regime where c is a large negative number, while the magnitude of the cosmological constant scales linearly with |c| and the length of the boundary of the disk is kept finite. In this regime, the gravitational path integral is dominated by a smooth geometry corresponding to a saddle point of the action. By systematically taking into account the quantum fluctuations about this saddle point, one can obtain a perturbative expansion of the partition function in powers of 1/|c|. I will present the results for the leading and the first subleading terms in this expansion.