I'm calling it early morning "Freewriting." - I started doing it (again) a few months ago, maybe just a little bit different than you described it.

So, my way...
I set up a timer for 10 minutes and start to write whatever is going through my mind. So, it's usually not some nice and easy to follow or even less meaningful story, but it's fun. I have a notebook for this Freewriting and I do it by hand, not on my PC and without the keyboard. Handwriting has an additional good impact on all of this (as far as I know.)

Anyways, I write down anything that crosses my mind at that moment. Sometimes it's even: "Why I'm doing this?"
The next one might be because of the noisy distraction from the outside, like: "Stupid motorcycle went down the street crazy loud."
Then something totally different goes through my mind, like: "OMG, I'm jotting here, losing my time and I still don't know what I'm going to cook today!"
And another one from nowhere would hit, like: "Why my daughter yesterday told me this and that, in fact?" - And so on and so forth.

However, your post just opened my eyes as I apparently have the problem with consistency. Went to check (as I write the date of writing in my notebook as well), and I just realized I haven't been doing it for last 2 months.

Therefore, thank you for reminding me to start again (for I don't know which time over)! 🙂
But it's really a good thing to do, as it somehow frees your mind and as well improves your writing skills although maybe totally unconsciously.