Is there a grammar rule for using 的 in this snippet 但是有意思的是? As I understand ...,但是有意思的是,... means ..., but the interesting thing is, ... but I went through great pains to arrive at this. The culprit here that jammed the cranks in my head was the 的. Had it not been there I might have just inferred that meaning and carry on assuming that the thing in interesting thing was implicit or the phrase was something akin to but what's interesting is.

What's 的 doing here? 

I'd also be grateful for another example showing the same rule in action.
Both your translations are definitely correct (if you think about it but the interesting thing and but what's interesting mean the same thing). As you pointed out, something is omitted here: in this case it's the word 事情 thing, the thing. This happens because it's implicitly inferred.

The sentence 但是有意思的事情是 is grammatically correct too and it means the exactly same thing. In this case we made 事情 explicit.

You already know that 的 introduces the modifier which precedes the noun that it's modifying. If you make 事情 implicit, you have to leave 的 in the sentence to indicate that the element that comes before represents a modifier, and the thing that is modified can be omitted.

Consider this sentence:


  我的自行车比你的新。
  My bike is newer than yours.


Let's analyse it:


  我的自行车 (Modifier + Subject) + 比 (preposition) + 你的 (Modifier) + 新 (Predicate)


In this example, after 你, there is a 的 that modifies something implicit. The word 自行车 is explicit the first time (after 我), but it's omitted the second time (after 你) because both the speaker and the audience know they are talking about bikes. Thus, you omit 自行车 the second time but keep 的 to signify that the element that comes before is a modifier.

P.S. Although it could sound redundant, it is perfectly OK to say 我的自行车比你的自行车新.