Feedback is a critical aspect of improvement. Unfortunately, when there is a lot of feedback from multiple sources, it can be difficult to distill the information into actionable insights. Consider student evaluations of teaching (SETs), which are important sources of feedback for educators. They can give instructors insights into what worked during a semester. A collection of SETs can also be useful to administrators as signals for courses or entire programs. However, on a large scale as in high-enrollment courses or administrative records over several years, the volume of SETs can render them difficult to analyze. In this paper, we discuss a novel method for analyzing SETs using natural language processing (NLP) and large language models (LLMs). We demonstrate the method by applying it to a corpus of 5,000 SETs from a large public university. We show that the method can be used to extract, embed, cluster, and summarize the SETs to identify the themes they express. More generally, this work illustrates how to use the combination of NLP techniques and LLMs to generate a codebook for SETs. We conclude by discussing the implications of this method for analyzing SETs and other types of student writing in teaching and research settings.