This work addresses maximally robust control synthesis under unknown disturbances. We consider a nonlinear system, subject to a Signal Temporal Logic (STL) specification and jointly synthesize the maximal possible disturbance bounds and the corresponding controllers that ensure the STL specification is satisfied under these bounds. Many works have considered STL satisfaction under given bounded disturbances yet, to the authors' best knowledge, this is the first work that aims to maximize the permissible disturbance set and find corresponding maximally robust controllers. We, therefore, introduce disturbance robustness as a model-based robustness metric for STL planning and control synthesis. We extend the notion of disturbance-robust semantics for STL, which is a property of a specification, dynamical system, and controller, and provide an algorithm for maximally robust controllers satisfying an STL specification using Hamilton-Jacobi reachability. We show its soundness and provide a simulation example with an Autonomous Underwater Vehicle (AUV).