Yes, it is a properly defined method of meditation.
Meditation isn't the absence of thoughts, but the awareness of them. Training the mind to a point when you can sit still without any thoughts is an extraordinary feat (which I suppose you're referring to as "blankness"), but in the Buddhist manner of training, it is also only the first step.
After you are keeping still, the second step is the single-pointed concentration or Samatha, where you keep your focus on one single activity/phenomenon, usually your breath.
Samatha is followed by Vipassana, i.e. meditation of insight, also sometimes called analytical meditation. From Samatha, you can move on to choose a phenomenon/event that you want to gain insight into (Buddhists usually contemplate on Buddha's teachings such as emptiness). Once chosen, you can move to dissect it pieces by pieces. It is important to retain the single-pointed concentration while doing this.
I personally as a practitioner prefer to be in Samatha for about 5-15 minutes, before I choose to go deeper into Vipassana. I have used it to analyze things such as my fear of house lizards or spiders. In here, I try to dissect the problem into smaller more precise questions such as:
Why I am scared of spiders > 1) They can kill me? 2) They can give me diseases? 3)They are ugly? 4) What makes they ugly? 5) Do they bring me any benefits?
I think dissecting the issues like this during meditation brings amazing clarity into irrational behavior, and helps us realize the emptiness of any being or phenomena existing from its own side.
The nun who taught me meditation once told me about how she would use the analytical meditation to think about the act of her boyfriend cheating on her, back when she had a lay life — an event which had an overbearing effect on her life.
She would dissect into smaller questions like "Was it the fact that he humped someone other than me?" "Is it the act of two sweaty bodies just going against each other that hurt me?" "Was it the breaking of the promise of exclusivity?" "Was it my sense of him "belonging" to me? Or, being my "possession" of sort?"
So, yes, you don't just have to sit still trying to avoid thoughts. The purpose of buddhist cultivation of mind is to gain insight into life, not avoid living.