We report on our experience with teaching software testing to graduate students. This experience was gained within a course offered yearly each winter term from 2015 till today. The course does not solely entail software testing as a topic, but also addresses briefly static analysis first (i.e. before testing) and verification afterwards (i.e. after testing). This is the reason for calling it with a twist from the testing perspective a sandwich approach. We motivate and present the overall structure and format of the course w.r.t. its learning objectives. We moreover describe some illustrative examples for structured interactions with students during the lecture as well as for project assignments, putting these into perspective w.r.t. the sandwich approach.