Implementations of the Belief-Desire-Intention (BDI) architecture have a long tradition in the development of autonomous agent systems. However, most practical implementations of the BDI framework rely on a pre-defined plan library for decision-making, which places a significant burden on programmers, and still yields systems that may be brittle, struggling to achieve their goals in dynamic environments. This paper overcomes this limitation by introducing an operational semantics for BDI systems that rely on Classical Planning at run time to both cope with failures that were unforeseeable and synthesise new plans that were unspecified at design time. This semantics places particular emphasis on the interaction of the reasoning cycle and an underlying planning algorithm. We empirically demonstrate the practical feasibility and generality of such an approach in an implementation of this semantics within two popular BDI platforms together with in-depth computational evaluation.