To do something in a plain, expressionless, or empty way is to do it blankly. If you gaze blankly into the distance, you have no expression on your face at all.
If you've ever made an announcement or given a speech only to have everyone stare blankly at you, you know exactly what this adverb means. People who look blankly at the TV set don't seem to be having much fun, and kids who gaze blankly at their math teacher don't appear to understand the equations she's writing on the board. Blankly comes from blank, which means both "bare or empty" and "void of expression."