Cognitive load classification is the task of automatically determining an individual's utilization of working memory resources during performance of a task based on physiologic measures such as electroencephalography (EEG). In this paper, we follow a cross-disciplinary approach, where tools and methodologies from speech processing are used to tackle this problem. The corpus we use was released publicly in 2021 as part of the first passive brain-computer interface competition on cross-session workload estimation. We present our approach which used i-vector-based neural network classifiers to accomplish inter-subject cross-session EEG transfer learning, achieving 18% relative improvement over equivalent subject-dependent models. We also report experiments showing how our subject-independent models perform competitively on held-out subjects and improve with additional subject data, suggesting that subject-dependent training is not required for effective cognitive load determination.