>> for nonrestrictive clauses that provide parenthetical information.

All nonrestrictive clauses that provide parenthetical information. I should have said ” for nonrestrictive clauses, which provide parenthetical information.”

I use “that” for restrictive clauses, which are an integral part of the sentence. I use “which” (separated by commas) for nonrestrictive clauses that provide parenthetical information.

It is pretty widely thought they are interchangeable or that “which” is merely more formal, but I think this leads to sloppy thinking and poor writing.

This has a nuance of “there may be other cookies that are 1) not on the counter and thus 2) not eaten by the speaker”.

Here “which” just introduces extra information.

This is a poor example (its almost bedtime!), but there are definitely cases where using “which” and “that” interchangeably will lead to unclear writing.

BTW: I have a question for you regarding the use of “that” and “which”. Some people are of the opinion that the two terms are interchangeable. Others–such as myself–believe that they are not, and that they serve two very different purposes. What’s your take?