The self-organization of turbulence is a remarkable property of flows with two sign-definite conserved quantities. When such flows are forced at small scales, a coherent flow called a condensate emerges, and is sustained by turbulence. The organizational principle for the condensate is that it should occupy the entire domain, respect its symmetries and be independent of small-scale details. One class of flows where condensation occurs is a rapidly rotating shallow fluid layer under the influence of gravity. This family of two-dimensional flows is characterized by a single parameter, the Rossby deformation radius R, which determines the range of influence of a flow perturbation. When R is much larger than the domain size, the flow reduces to two-dimensional Navier-Stokes. In the opposite limit of vanishing R, a regime termed LQG, interactions between fluid elements become strictly local. We uncover an unexpected organizational principle in the latter: the condensate area is determined by the ratio between the forcing scale and the UV cutoff. In particular, the large-scale flow can take different configurations depending on this ratio, including regions of bi-stability of configurations and spontaneous symmetry breaking in the thermodynamic limit (increasing system size). We explain how this behavior arises from the spatial distribution of fluxes of the conserved quantities in the system.