The gold standard would be to make each student do an oral defense of their work. Hand-written exams are good too. Both of these approaches are time-consuming to mark, though.
Assessment design can require students to perform analysis of rare and obscure source material, so that there are no published materials for AI to draw on (which can make it struggle). Similarly, asking for a good bibliography that lists the sources used in the text and formats it correctly would show up the hallucinatory tendencies of AI, I think — though I haven’t tried the latest models.
Yes — I think if I were to teach a large undergraduate class tomorrow I would go with a combination of handwritten exams and, for homework assignments, critical analyses of the most obscure examples of whatever is being studied possible so that AI has no idea what you’re even on about (in my field, ask it to analyse music; it’s hopeless). Multiple choice is fine for stuff that can be rote learned.