  We propose a microscopic definition of finite cut-off JT quantum gravity on
the disk, both in the discretized and in the continuum points of view. The
discretized formulation involves a new model of so-called self-overlapping
random polygons. The measure is not uniform, implying that the degrees of
freedom are not in one-to-one correspondence with the shape of the boundary.
The continuum formulation is based on a boundary $\text{CFT}_{1}$ from which we
predict some critical exponents of the self-overlapping polygon model. The
coupling to an arbitrary bulk matter CFT is also discussed.
