CBT (Cognitive Behavioral Therapy) is a rather complex, in-depth subject that a councelor would use primarily in individual therapy to help a person change their patterns of thoughts, feelings and actions. If one of those three things changes, the other two shift as a result. People who work with clients with CBT typically have to have a masters or doctoral degree just focusing on mental health. Like a licensed clinical social worker. States regulate the scope of practice as to who can provide what kinds of therapy.
Most of the OT curriculums I've seen have 1-2 courses on mental health, sometimes broken down by adult, or pediatric. I've heard a couple mental health OTs talk about what they do, and a lot of it sounds like therapeutic group activities. Doing these activities allows the OT to get a look at how a person is functioning cognitively or physically instead of relying on self-report, which may be inaccurate. Historically, OT mostly started in mental health, and in the UK, half of all OTs work in mental health. Basically, the US health care system does not have a lot of funding for mental health, and OT is underutilized in that area.