In this paper we propose and numerically study a neuromorphic computing scheme that applies delay-based reservoir computing in a laser system consisting of two mutually coupled phase modulated lasers. The scheme can be monolithic integrated in a straightforward manner and alleviates the need for external optical injection, as the data can be directly applied on the on-chip phase modulator placed between the two lasers. The scheme also offers the benefit of increasing the nodes compared to a reservoir computing system using either one laser under feedback or laser under feedback and optical injection. Numerical simulations assess the performance of the integrated reservoir computing system in dispersion compensation tasks in short-reach optical communication systems. We numerically demonstrate that the proposed platform can recover severely distorted 25 Gbaud PAM-4 signals for transmission distances exceeding 50km and outperform other competing delay-based reservoir computing systems relying on optical feedback. The proposed scheme, thanks to its compactness and simplicity, can play the role of a monolithic integrated hardware accelerator in a wide range of application requiring high speed real time processing.