Learn Italian: Quello che dice è solo una sciocchezza fastidiosa.

When "what" means "that which" or "the thing that" in a statement, you cannot use the question word cosa. You have to use quello che (literally "that which") or its slightly more formal equivalent, ciò che.

How is the noun sciocchezza formed?

It is built from the adjective sciocco, which means "silly" or "foolish". By adding the suffix -ezza (which works like "-ness" in English), it becomes an abstract noun meaning "foolishness" or "nonsense".

Since this lesson is about verbs like smetterla, how would you tell this person to "stop it"?

You would use the imperative form of one of the cessation verbs, such as Smettila!, Piantala!, or Finiscila!. The fixed pronoun la in these verbs perfectly captures the idea of stopping a specific annoying situation or behavior, like spouting a sciocchezza fastidiosa.

Could the adjective fastidiosa be placed before the noun?

It could be, as una fastidiosa sciocchezza, but it sounds much more natural after the noun. Placing it after emphasizes the literal, descriptive quality of the annoyance, which fits everyday conversation better than putting it before the noun, which can sound slightly dramatic or poetic.