We approach aspect-based argument mining as a supervised machine learning task to classify arguments into semantically coherent groups referring to the same defined aspect categories. As an exemplary use case, we introduce the Argument Aspect Corpus-Nuclear Energy that separates arguments about the topic of nuclear energy into nine major aspects. Since the collection of training data for further aspects and topics is costly, we investigate the potential for current transformer-based few-shot learning approaches to accurately classify argument aspects. The best approach is applied to a British newspaper corpus covering the debate on nuclear energy over the past 21 years. Our evaluation shows that a stable prediction of shares of argument aspects in this debate is feasible with 50 to 100 training samples per aspect. Moreover, we see signals for a clear shift in the public discourse in favor of nuclear energy in recent years. This revelation of changing patterns of pro and contra arguments related to certain aspects over time demonstrates the potential of supervised argument aspect detection for tracking issue-specific media discourses.