Facial hair is a defining trait of personal identity, yet remains a critical bottleneck for digital avatars. Recent volumetric methods achieve photorealism but bake hair into the underlying face geometry, preventing editability and failing to resolve sparse, strand-like structures. Meanwhile, scalp-hair reconstruction methods target dense hair volumes and do not transfer to the sparse, spatially-varying nature of facial hair. We present a pipeline that automatically reconstructs facial hair -- beard, mustache, lashes, and brows -- from multi-view images, converting an unstructured 3D Gaussian representation into an explicit curve-based strand representation. We resolve geometric ambiguities in four stages: (i) optimizing 3D Gaussians constrained by tracked head geometry to enforce early ray termination and suppress sub-surface noise; (ii) tracing continuous strands robust to frequent crossings and extreme curvature; (iii) grounding strands to the surface and resolving root-tip ambiguity via a physically-motivated prior; and (iv) refining the reconstruction through opacity-driven density control under photometric optimization. To our knowledge, this is the first method to reconstruct high-fidelity facial hair strands from a 3D Gaussian representation. The recovered strands faithfully preserve the orientation and sparsity patterns characteristic of facial hair, and yield assets immediately suitable for downstream production tasks, including facial animation and physical simulation, geometric grooming and transfer, appearance editing, and physics-based rendering.