Neuromorphic computing, an innovative field in electronic and computing engineering, aims to enhance computing paradigms by simulating brain processes. Memristors, a two-terminal device, hold promise in revolutionising neuromorphic architectures by circumventing the Von-Neumann bottleneck. The performance and applicability of memristors heavily rely on the materials and fabrication processes employed. Graphene exhibits unique properties that can be leveraged in memristor design. Moreover, graphene stands out as a material with the potential for large-scale, sustainable production through Plasma Enhanced Chemical Vapour Deposition (PECVD). Notably, the properties of graphene-electrode memristors vary with minor structural differences induced by different PECVD temperatures. This paper reports the synthesis of graphene electrodes by time- and cost-effective PECVD from a sustainable plant extract for memristors. In addition, this paper delves into investigating how these structural variations impact the properties of graphene memristors and explores their potential exploitation in neuromorphic applications for implementing the well-known Spike Timing Dependent Plasticity (STDP) learning mechanism. The paper also utilises the developed STDP learning to perform an unsupervised spike-based pattern classification task.