Drowsiness monitoring can reduce workplace and driving accidents. To enable a discreet device for drowsiness monitoring and detection, this work presents a drowsiness user-study with an in-ear EEG system, which uses two user-generic, dry electrode earpieces and a wireless interface for streaming data. Twenty-one drowsiness trials were recorded across five human users and drowsiness detection was implemented with three classifier models: logistic regression, support vector machine (SVM), and random forest. To estimate drowsiness detection performance across usage scenarios, these classifiers were validated with user-specific, leave-one-trial-out, and leave-one-user-out training. To our knowledge, this is the first wireless, multi-channel, dry electrode in-ear EEG to be used for drowsiness monitoring. With user-specific training, a SVM achieved a detection accuracy of 95.9%. When evaluating a never-before-seen user, a similar SVM achieved a 94.5% accuracy, comparable to the best performing state-of-the-art wet electrode in-ear and scalp EEG systems.