This paper presents a new paradigm to simultaneously optimised the topology and anisotropy of a continuum under prescribed boundary conditions (BCs). The goal is to find the optimal topology, local elastic symmetry and orientation of the main orthotropy axes of a variable-stiffness composite (VSC) structure with variable thickness, which maximises the stiffness subject to a volume constraint. The approach employs density-based topology optimisation, the polar method to represent anisotropy, and non-uniform rational basis splines (NURBS) entities to describe the different fields. NURBS entities allow avoiding the checkerboard effect and mesh-dependency of the solution, they are compatible with CAD software and facilitate the fomulation of technological constraints. The polar method allows expressing any planar tensor to invariants related to the elastic symmetries of the tensor and simplify the expression of the tensor when considering affine transformation. The proposed approach is tested on benchmark problems under inhomogeneous Neumann-Dirichlet BCs, exploring various factors influences on the optimised solution, such as penalty scheme, loading conditions, inclusion of local thickness as a design variable, optimization strategy, and NURBS entity parameters.