Electric vehicle (EV) routing faces significant operational challenges due to limited driving range, charging constraints, and uncertainty in energy consumption. This project addresses the Electric Vehicle Routing and Overnight Charging Scheduling Problem under energy consumption uncertainty, assuming exclusive depot-based overnight charging. Energy consumption on each arc is modeled as a bounded random variable and incorporated through a budgeted robust optimization framework. The resulting problem is solved using a Branch-and-Price-and-Cut algorithm based on a route-based set partitioning formulation. Robust feasibility is ensured directly within the pricing problem through an adapted labeling algorithm, while subset-row cuts and an enhanced hierarchical branching scheme accelerate convergence. Computational experiments highlight the trade-off between routing cost and protection against uncertainty, and demonstrate how robustness impacts charging schedules and route departure times.