I have a 1906 wood frame house with a single-course brick exterior in Minnesota. I've discovered that there is a sub wall half way between the sheathing and the interior plaster and lathe. I'd estimate there is about 3 inches on either side of the wall of uninsulated space. Is this sub wall construction common?

What would be the best approach to insulating one or both sides of that wall, especially given the brick exterior?
Would insulating one side provide enough benefit?