Fans often refer to the fan-cut version as "Naruto Kai." This is essentially the "good piece" you are describing. It cuts the series down from 500 episodes to roughly 300 episodes . It creates a viewing experience comparable to Attack on Titan or Fullmetal Alchemist: Brotherhood —dense, plot-focused, and satisfying.

There is one counter-argument to removing all filler. There are segments known as "semi-filler" or "light filler" that the anime studio used to pad out time while the manga caught up.

If you want to experience the tight, high-quality version of the story, here is the essential viewing guide. The numbers refer to the original episode count so you can skip accordingly.