Recent scaling theories for the eddy fluxes in the two-layer quasi-geostrophic (QG) model assume a flat bottom boundary. Here, we discuss an organizing principle for how rough topography (i.e., topography with length scales similar to or smaller than the eddy scale) modifies the fully developed state of baroclinic turbulence. In particular, we focus on random, homogeneous topography in the two-layer QG model on an 𝑓-plane, forced by a zonal shear and dissipated by Ekman drag. We present a suite of numerical simulations using idealized monoscale topography, systematically modifying the topographic length and height scales and the strength of the drag. We outline the dependence of the eddy diffusivity, 𝐷, velocity scale, 𝑉, and mixing length, ℓ, on the two nondimensional control parameters: 𝜅 * , controlling the strength of the drag, and ℎ * , controlling the strength of topographic-advective interactions. Two distinct regimes are identified and quantitatively predicted by a regime transition parameter, 𝛼, which depends on both 𝜅 * and ℎ *. Once 𝛼 surpasses a critical value, all eddy scales are reduced below their flat bottom values and become much less sensitive to the drag. Spectral energy budgets reveal that energy pathways are importantly reorganized in this regime compared to the flat bottom limit. We show how this phenomenology extends to more realistic, multiscale topography and to three-layer QG simulations.