You can do both and in fact they complement each other. Doing things fast allows you to do more iterations of experimenting/thinking, before you commit to your final solution. If you work slowly, you usually have to rely on your first intuition, because you don't have time for anything else. If you work fast, you can do more work up front, evaluate more options, test for more edge cases, etc. It helps you get a better picture of the problem you are trying to solve and that is what the "slow thinking" is about.
If you have the impulse to go fast, think about prototyping whatever it is you are trying to do, if you can. You should agree with yourself to dispose of the prototype completely. By the time you've gone through debugging the prototype you'll know much of what is needed to do the real thing.
Obviously, this doesn't always work. In those cases, whiteboards, pen and paper, even a text document can help.
I don't think those things are at odds. To be fast habitually you have had to slow down to pave the pathways for speed. What most organizations miss out on is thinking they can go fast without paving the way first. In all disciplines the fundamentals never come cheap or fast but once they are there then you can go as fast as you want and you can do it confidently.
Speed is important. Patience is important. Stepping back and smelling the flowers is important. It's not about fast or slow. It's about right, and you can't be right all the time if you're stuck in the habit of zooming along all the time.
I remember how many _years_ it took Apple to figure out how to do right-click properly while their competitors were speeding along with that silly second button.
I honestly didn't realize that Apple ever figured that out. I started out on Macs (Mac+), but haven't had one since the '90s. I used one earlier this year trying to do stuff for my cousin on her machine. That mouse was truly bizarre. You'd accidentally touch it a certain way and weird shit would happen.
I'm sure it's great once you learn it and get used to it, but not exactly intuitive.
Speed as a habit seems like it would ruin the ability to slow-think. Is there a dichotomy here or can we do both?