My therapist is very blank-slate. She has allowed me to know very little about her. But over time, I've actually been able to feel quite close to her.

The dynamic can feel odd and it is certainly unique. If you are new to therapy I would encourage you to give it a chance. If not with her, then with someone else. Therapists also vary quite a bit in terms of how much they self-disclose. Maybe you need a therapist who discloses enough so that you feel that human connection. That could even be something you bring up with your current T. As a therapist, I start off disclosing very little but will disclose slightly more if the client expresses that it is helpful.