Algorithms at the intersection of computer graphics and medicine have recently gained renewed attention. A particular interest are methods for virtual surgery planning (VSP), where treatment parameters must be carefully chosen to achieve a desired treatment outcome. FEM simulators can verify the treatment parameters by comparing a predicted outcome to the desired one. However, estimating the optimal parameters amounts to solving a challenging inverse problem. In current clinical practice it is solved manually by surgeons, who rely on their experience and intuition to iteratively refine the parameters, verifying them with simulated predictions. We prototype a differentiable FEM simulator and explore how it can enhance and simplify treatment planning, which is ultimately necessary to integrate simulation-based VSP tools into a clinical workflow. Specifically, we define a parametric treatment model based on surgeon input, and with analytically derived simulation gradients we optimise it against an objective defined on the visible facial 3D surface. By using sensitivity analysis, we can easily explore the solution-space with first-order approximations, which allow the surgeon to interactively visualise the effect of parameter variations on a given treatment plan. The objective function allows landmarks to be freely chosen, accommodating the multiple methodologies in clinical planning. We show that even with a very sparse set of guiding landmarks, our simulator robustly converges to a feasible post-treatment shape.