Avoiding clumps in cacio e pepe? I've been trying to make a very basic three-ingredient cacio e pepe over the last few days and have found it difficult to create a smooth, creamy sauce.

I'm using only two cups of microplane-grated pecorino romano cheese, a handful of spaghetti, and crushed black pepper. Salt in the pasta water, too, of course.

I've tried it two ways and gotten varying results:


Cooking the pasta shallow water in a wide pan to concentrate the starch. Then, drain, lower the heat and add the pasta back in with a few ladles of water and adding the cheese gradually, tossing stirring violently with a wooden spoon.
Add some of the pasta water to the cheese in a separate bowl a few minutes before the pasta finishes cooking. Whisk the pasta water and cheese into a paste, then add the finished pasta to it with some extra water and, again, stir like crazy.


Neither seems to work very well, though my best results so far came from (1), but I'm quite convinced it was luck. What might I be doing wrong or overcomplicating? Everything I see on the Internet says it should be "very easy", but the lack of videos showing this recipe has made it difficult to learn. The videos I have seen use a lot of olive oil and butter, which I'm told is absolutely not traditional or okay.
Achieving a creamy sauce for cacio e pepe, and dishes like it (carbonara comes to mind) is not as straight forward as some would have you think. Fortunately, while we strive for the perfect emulsification, those attempts that don't exactly work are still delicious.  

Here are some tips:
(1) Make sure your cheese is grated as finely as possible, and that it is at room temperature or warmer.  A microplane is perfect. 

(2) The water you add can't be too hot.  Scoop some pasta water out halfway through the cooking process, allow it to cool, and use that to add later.  

(3) Drain pasta and allow to cool a minute before dressing. 

(4) Some find that combining pasta and cheese in a cool pan is better (so that you can control heating). 

(5) Some combine the water and the cheese, then add that mixture to the pasta.

(6) The addition of fat (butter, cream, oil) helps the cheese to emulsify, but this addition varies and is sometimes not included.  

It's all about practice and adjustment.  Much of this information came from here, and I can vouch for more success (sadly,not perfection) using these techniques.