Unlike MOOCs, which mainly expect students to use resources online to
    complete courses themselves, competency-based programs depend on faculty
    mentors to walk learners through the learning process. It’s almost the
    opposite of the university lecture. Rather than a professor talking to a
    roomful of students, a professor talks to students one-on-one while they
    learn information at their own pace.

This sounds almost exactly like the 'tutorial' system used for a thousand years (for undergraduates) at Oxford and Cambridge. Students meet with their tutors weekly and are given suggested reading, and usually an essay to write. Once a term, proctored exams are held.

Edited to add: One difference between university in the U.S. and U.K. is that in the U.K., 'breadth' classes are almost unheard of; the idea of a chemistry major taking an anthropology class, a psychology class, or an art class is strange. That's one of the reasons undergraduates there finish in three years, usually.