I'm teaching a university math course next semester and I've been messing around with a solution to this that my old analysis professor used to employ. Every week, they take home a handful of theory questions. These aren't turned in for credit. But, every week, there'll be a short quiz where one of those questions are asked verbatim, along with a small follow up.

That felt like a very natural solution to me. Of course, worst case scenario, they just blindly generate and memorize the proofs without thinking. But I think the follow ups will catch them in that case. Moreover, I choose to believe that >90% of my students are willing to at least put in the work of scrutinizing those proofs which is honestly not bad exercise in its own right.

I would love to do oral exams directly, the logistics with the number of students I have just make that hard. I know we're trialing it with the less populated special topics courses.

Only as an honor system for students who want to learn the material.

But worthless for assessments and assigning grades.