Cell-free massive multiple-input-multiple-output (CF-mMIMO) is regarded as one of the promising technologies for next-generation wireless networks. However, due to its distributed architecture, geographically separated access points (APs) jointly serve a large number of user-equipments (UEs), there will inevitably be a discrepancies in the arrival time of transmitted signals. In this paper, we investigate millimeter-wave (mmWave) CF-mMIMO orthogonal frequency division multiplexing (OFDM) systems with asynchronous reception in a wide area coverage scenario, where asynchronous timing offsets may extend far beyond the cyclic prefix (CP) range. A comprehensive asynchronous beam-domain signal transmission model is presented for mmWave CF-mMIMO-OFDM systems in both downlink and uplink, incorporating phase offset, inter-carrier interference (ICI) and inter-symbol interference (ISI). To address the issue of asynchronous reception, we propose a novel per-beam timing advance (PBTA) hybrid precoding architecture and analyze the spectral efficiency (SE) in the beam domain for downlink and uplink asynchronous receptions. Both scalable centralized and distributed implementations are taken into account, and the asynchronous delay phase is utilized to design precoding/combining vectors. Furthermore, we formulate the sum rate maximization problem and develop two low-complexity joint beam selection and UE association algorithms considering the impact of asynchronous timing offset exceeding the CP range. Simulation results demonstrate that the performance will be severely limited by ICI and ISI, and our proposed PBTA hybrid precoding architecture effectively mitigates asynchronous interference compared to the nearest AAU/UE-based timing-advance scheme. Additionally, numerical results show that our proposed low-complexity joint beam selection and UE association algorithms achieve superior SE performance.