Is it "stern talking too", or "stern talking to"?

Merriam-Webster and the New Oxford American Dictionary say it's a stern talking-to, with a hyphen.

If you're fine with talking to someone frankly, you tend to phrase it in terms of, well, just talking to them.

I will have to talk to Bob.
I will have to give the same talk to Sue.
I will have to give that talk to Greg, too.
I will also be talking to Fred.

Most people who use a talking to as a noun do so to describe some chore or other unpleaseant responsibility.

Gracie wet the bed. I will have to give her a talking to.

Knowledgeable English scholars are able to tell the difference.

I tried to talk to Molly, but she was too busy listening to Diane. Now I need to give Diane a talking to too.

Talking to is an old-fashioned verb form (or nounification, if that's a word*) that reflects the idea that superiors talking to a junior were talking to them, not with them.

Hence, if you would like to have a better relationship with your inner self, you're probably better off conversing or discussing or, heaven forbid, understanding. If you don't have such a good relationship with your inner self you could encourage or cajole or persuade. To give yourself a stern talking to is a sign that you regard your subconscious mind as a child. You're probably better off giving yourself some encouragement and a stern talking to too.

*Oh, wow, it is.